I fully agree, they are mechanically alternate names, though I would say they are alternate names for the same set of bonuses, rather than for the same martial art style.
I think where our opinions differ, is I believe it's possible for someone to know multiple martial arts that have the same mechanical bonuses, thus allowing them to be taken more than once, and you believe that if you have any one martial art, you can't take it's alternative styles. I think this comes down to a GM decision that will change from game to game, as RAW I can't find anything that says it can't be done.
I do believe that there can be an argument made for someone having both Brazilian Jiu-Jitsu and Wrestling (it's a common feature among MMA fighters) and think that mechanically in-game it doesn't unbalance Martial Arts. That said, I think we've taken this well off-topic, I just wanted to give Ympulse another option to get his +3DV, but it doesn't sound like his GM would be open to it anyway.