It's a new game with some new gimmicks.
The new game and the original pushmo don't have the falling blocks gimmick of crashmo - that's one difference...
In Pushmo World, aside from a new single player set of puzzles, there's a training area and a mystery puzzle area. Mystery puzzles have unique gimmicks, like pulling a block of a certain colour making all matching colours move too.. there are timed challenges etc. Puzzles can have their own rules. There's a placeholder menu option under pushmo world fair for more Nintendo developed puzzles, and the community puzzles have been pretty high standard so far..
My only complaints are the tutorial levels (if you've been through them in pushmo and crashmo you're probably bored of them by now) and the oversight of not being able to filter community designs by your friends list, you can only sort by newest or most popular. You CAN skip any level at any time for the tutorials though and hopefully there's a patch in future for better browsing of world fair.