[Odsh]

According to the rules:

Burning
[...]
There are multiple ways to remove this status. You can spend a Major Action and roll an Agility + Reaction (2) test; success means the fire is out and the status is removed. You can also jump into water to remove the status without a roll.
If you gain the Wet and/or Chilled statuses, the Burning status is canceled.

Corrosive
[...]
Can be removed with certain gear (like baking soda for acids!) and equipment. The Wet status does not necessarily remove it, as some chemicals continue burning the skin even after contact with water. The gamemaster can determine when enough water has been applied to remove the chemical in question.

I don't know what that "certain gear" is and I don't think a runner usually carries baking soda around. You can certainly put Chemical Protection and Fire Resistance on your armor, but that prevents the status from being applied in the first place, not removing it once it has been applied.

Bottom line is, Corrosive seems to be a much more severe status than Burning since you can't get rid of it that easily. If you don't have "enough water" or "baking soda" to wash it off, you're entirely dépendent on the GM's goodwill to decide when the effect wears off naturally.

EDIT: or a mage with the Cleansing Heal spell

Which makes the Acid Stream and Toxic Wave spells much more lethal than the Flamestrike and Fireball spells - for the same drain value. Icing on the cake, the chemical damage from Acid Stream and Toxic Wave can permanently decrease an armor's effectiveness - which fire damage cannot do.

How do you handle this in your games? I'm tempted to just allow removing Corrosive with the same Major Action and Agility + Reaction (2) test as for removing Burning.

[Xenon]

In previous edition instant combat spells typically didn't have any lasting elemental effects. The magical fire from the fireball would vanish after the initial impact (but highly flammable objects could still be set on fire and burn on their own). The magical acid from toxic wave would typically quickly evaporate after the spell landed.

If you wanted to cause something to actually burn you would instead use a permanent manipulation spell that you had to sustain for a number of Combat Turns before the target was ignited (and was basically given the Burning status).

This seem to have changed for this edition.

I'm tempted to just allow removing Corrosive with the same Major Action and Agility + Reaction (2) test as for removing Burning.

This never came up for us.

But if balance is of concern here I guess you could house rule that the secondary effect from Flamestrike/Fireball is a lasting Burning status effect while the secondary effect from Acid Stream/Toxic Wave is that it (just) permanently reduce armor rating (no lasting Corroded status effect). ...or that the Corroded status effect only last for short period of time (one Combat Round, for example).

[Odsh]

...or that the Corroded status effect only last for short period of time (one Combat Round, for example).

I like that one, it remains simple and each damage type has its specificities.
Fire for a long lasting damage over time, but can be cancelled early with an action and a successful test.
Chemical for a short duration damage over time and potential armor reduction, but cannot be cancelled early (unless you jump in a pool of water or something).

[Stainless Steel Devil Rat]

...

Bottom line is, Corrosive seems to be a much more severe status than Burning since you can't get rid of it that easily. If you don't have "enough water" or "baking soda" to wash it off, you're entirely dépendent on the GM's goodwill to decide when the effect wears off naturally.
...

How do you handle this in your games? I'm tempted to just allow removing Corrosive with the same Major Action and Agility + Reaction (2) test as for removing Burning.

For starters:  there's nothing wrong with being entirely dependent on GM goodwill for ending statuses.  That's basically the RAW

If you want to add rules for Corrosive, there's nothing wrong with the suggestions above. Personally I think "1 round and it ends without you having to do anything to end it" is too short and too easy, but of course YMMV.

A couple of other suggestions:

1) My go-to on this issue would be to just say a medkit reasonably does have some salve that meets the "baking soda or similar" test.  Expend a unit of supplies from your medkit, and boom. Easy Peasy Lemon Squeezy.

2) As Xenon mentioned, the actual metaphysics of spells (especially Direct spells, and double especially Area Direct spells) has changed in a few ways that contradict all previous editions, but in explicit ways so they're clearly not changes by accidental omission.  Basically, the only difference between now Direct and Indirect combat spells is what dice pool you use to resist them. Armor now helps vs Direct combat spells and so it stands to reason that a corrosive combat spell leaves the burning primarily on your outer clothing.  Just as if you've been sprayed with Xenomorph blood, what you *do* is shuck those outer garments immediately, which I would say helps (or completely) mitigates the corrosive status.

[Xenon]

Basically, the only difference between now Direct and Indirect combat spells is what dice pool you use to resist them. Armor now helps vs Direct combat spells ...

By less strict reading of RAW and looking more into plausible RAI to make some sense out of it we ruled it as such:

• Defense Rating against Physical based Combat Spells (which can only be cast on the material plane) is typically Body + Armor.
• Defense Rating against Mana based Combat Spells (which can only be cast on living subjects) is typically Intuition + Innate Armor.

SR6 p. 131 Spell Descriptions
Mana spells interact solely with the astral plane; they may affect living beings, as living beings have an astral component, but they have no effect on nonliving, non-astral entities.

SR6 p. 132 Combat Spells
Defense Ratings are as normal, depending on if the defender is on the material plane or astral plane (see p. 161).

SR6 p. 161 Astral Combat
...your Defense Rating does not involve physical armor or your Body attribute; instead, it’s Intuition + innate armor + armor effects (such as the Mystic Armor spell, p. 141).

SR6 p. 141 Mystic Armor
Your magic fills the astral form of the target, hardening it and making it better able to absorb damage. Roll Sorcery + Magic and add net hits to target’s Defense Rating when in astral combat or against mana-based Combat spells.

[Odsh]

For starters:  there's nothing wrong with being entirely dependent on GM goodwill for ending statuses.  That's basically the RAW

You're right of course. Let's say I worry more about consistency. Why would a Toxic Wave inflict varying durations of the Corrosive status depending on the mood of the GM? I prefer when the players know beforehand what they're up against or how their spells will behave. And if you want consistency, the house rule is not far.

Basically, the only difference between now Direct and Indirect combat spells is what dice pool you use to resist them.

To me it's a bit more than that. The main difference is that direct combat spells only inflict net hits + amp up damage, whereas indirect combat spells inflict (Magic/2) + net hits + amp up damage. To balance that out, only the damage from indirect combat spells can be resisted (with Body). Direct combat spells "pierce" any resistance after the defense test. In that regard, they're an exception to the general attack / defense / resistance mechanics.

Armor now helps vs Direct combat spells and so it stands to reason that a corrosive combat spell leaves the burning primarily on your outer clothing.

I suppose you mean indirect combat spells. There is no direct combat spell that inflicts elemental damage a.f.a.i.k.

[Stainless Steel Devil Rat]

For starters:  there's nothing wrong with being entirely dependent on GM goodwill for ending statuses.  That's basically the RAW

You're right of course. Let's say I worry more about consistency. Why would a Toxic Wave inflict varying durations of the Corrosive status depending on the mood of the GM? I prefer when the players know beforehand what they're up against or how their spells will behave. And if you want consistency, the house rule is not far.

Well, I wouldn't say "GM Discretion" necessarily means "GM mood".  GM discretion about a spell-inflicted status of indeterminate length can (and I daresay should) factor in circumstances like number of net hits, relevant defensive gear, the environment/atmosphere, and etc.  The third leg of the Edge triad, Circumstantial Edge, already works in this "GM Discretion" methodology.  I don't think there's a need to make status durations be any more rigid than that... but I acknowledge that YMMV.

[Shinobi Killfist]

I'd probably treat their durations the same, acid would be a better spell for direct damage due to this but fire would have potential to spread outside of its area and could interact in more entertaining ways with explosive etc.

[MercilessMing]

I suppose you mean indirect combat spells. There is no direct combat spell that inflicts elemental damage a.f.a.i.k.

That's correct, and Street Wyrd reinforces this.  For the best example, compare the Blood Magic spells "Boil Blood" vs "Chilled Claret" on page 159-160. 
Thematically, one heats the blood and one chills the blood.  Chilled Claret invokes Hobbled and Dazed, but no elemental factor and it's a Direct Damage spell.
Boil Blood invokes Burning and Bleeding, and it's Indirect.  To account for this, the spell description describes pulling blood out and then shooting it back at the target (so there's something to Dodge).

[Stainless Steel Devil Rat]

Another thought from Street Wyrd:

You can design a spell to end statuses, so if you only have statuses only last a few rounds that's putting a 2nd order negative impact on the value of such spells.

[Shinobi Killfist]

I suppose you mean indirect combat spells. There is no direct combat spell that inflicts elemental damage a.f.a.i.k.

That's correct, and Street Wyrd reinforces this.  For the best example, compare the Blood Magic spells "Boil Blood" vs "Chilled Claret" on page 159-160. 
Thematically, one heats the blood and one chills the blood.  Chilled Claret invokes Hobbled and Dazed, but no elemental factor and it's a Direct Damage spell.
Boil Blood invokes Burning and Bleeding, and it's Indirect.  To account for this, the spell description describes pulling blood out and then shooting it back at the target (so there's something to Dodge).

Really?  It pulls out your blood and shoots it back at you?

Sigh...

[Xenon]

Street Wyrd reinforces this. 

Does it mention anything about DR against Direct Combat spells?

While not very clear, the intention in cbr seem to be that it is equal to Intuition (not your physical Body as it is for Indirect Combat spells) + Innate Armor (including Mystic Armor, but not physical armor as it is for Indirect Combat spells).

[Stainless Steel Devil Rat]

I would have liked to have seen some sort of AR vs DR evaluation take place for all spells, not just combat spells.  But Street Wyrd didn't discuss this leg of edge gain whatsoever (that I noticed).  So, no it didn't revisit the categorical rules for combat spells. 

At least not directly.

I did notice at least one instance where an Area Direct Combat spell only affected targets the caster could see.  Having to be able to see the target (for Direct spells) was a restriction that was omitted from the CRB, so that's interesting.  Throw some evidence on the side of that omission being inadvertent, rather than a deliberate change. Unless of course, the writer of the relevant passage in Street Wyrd was simply erroneously carrying over obsolete baggage from 5e...

[Xenon]

an Area Direct Combat spell only affected targets the caster could see. 

This was [still] the default blanket behavior of all LOS(A) spells in crb as well.

SR6 p. 131 Spell descriptions - Range
LOS, meaning the caster needs a physical sight line to the target (optical lenses such as binoculars count as physical line of sight; magical effects and digitized images such as thermographic goggles do not);
LOS(A) means the spell has a line of sight range and also has an area effect, which starts at a two-meter-radius sphere;

[Shinobi Killfist]

an Area Direct Combat spell only affected targets the caster could see. 

This was [still] the default blanket behavior of all LOS(A) spells in crb as well.

SR6 p. 131 Spell descriptions - Range
LOS, meaning the caster needs a physical sight line to the target (optical lenses such as binoculars count as physical line of sight; magical effects and digitized images such as thermographic goggles do not);
LOS(A) means the spell has a line of sight range and also has an area effect, which starts at a two-meter-radius sphere;

From that its not clear if you need line of sight for each target or just the spot you place the area.