Dirt jumping vs BMX vs MTB

I see that different bikes are sold for the three different purposes.

I see they and their wheels sort of get bigger from BMX < DJ < MTB.

And the seat gets more redundant (?) in the same order.

From a noob's standpoint, the courses BMX and DJers ride look relatively similar from dipping into youtube videos. And then some of the MTBers encounter similar undulations, but naturally occuring. What this guy is doing http://www.youtube.com/watch?v=J7dnXiNBDXE I find really exciting.

I guess I'm wondering, how do the different anatomies of the bikes correspond to the variances in demand in the three disciplines?

As I can't quite see why the guy in the video doesn't use a dirt jumping bike, or even a BMX one for that matter. Or can you use any bike for any discipline - can you dirt jump or go on a BMX track on a MTB?

The reason I'm curious is, I have a MTB and am thinking of getting a BMX or a DJ bike, but I'm not sure I would need one - can you learn most things on a MTB and then move to a BMX when you get really good, or is it the other way round, or do you have to be really specific about which kind of ground you want to work on.

If there's like a clear youtube vid for each discipline that I can be pointed to that would be good too, as I think I'm confusing myself! :confused:

Thanks.