[Senko]

As the topic says is the program limit for how many programs a decker can have or on how Many they can have running at any one time?

[Lanaya]

It's for the number you can run at a time. Your deck can contain as many inactive programs as you can afford.

[DWC]

Given that programs are basically free relative to the massive cost of cyberdecks, it's no surprise that you can have them all on your cyberdeck all the time.

[Xenon]

is the program limit for how many programs a decker can have

No.
You can own all of them.

or on how Many they can have running at any one time?

Yes
A cyberdeck is limited on how many cyberprograms it can run at once.
This is listed on the Cyberdecks table on SR5 p. 439
It is a free matrix action to unload or load a cyberprogram on your cyberdeck.