What are the main differences between R1 and R2?

In the any% speedrun is no difference except for the escape. In R2 the scooter section is different in escape.

Also the platforms at the beginning fall down faster, he removed some platforms to get to the paragoomba, and pillars is harder because of the distance between the platforms

And what about the other categories?

I don't really know, you should probably ask the developer.