What is the different between PSP 1001 and1000?

The 1000 part is the model (phat) and the number at the end is the region. 1000 is Japan, 1001 is North America, 1002 is Australia/New Zealand, etc. PSP's are region locked when it comes to UMD movies, so that's really the only difference. You could not play a US movie UMD on a PSP-1003 (UK region), though the games are region free and work on any region PSP.