Hi Daphuon2,
At first sight they are equal, and they are.
The Home Edition is the replacement for 9x and ME. The Proffesional Edition is the replacement for the 2k and NT. The Corporate version can be XP Home Edition or Professional Edition. Confusing? Well, not really, The Corporate Edition is used by Computer sellers. In other words, its used to install it on your PC when you buy the Computer, and that's why it can be one or the other. So the best to have, is the Professional edition with a Corporate Key.
There is another version, with another name, Windows.net. This is the "replacement" for the 2k Server's Editions. The real replacement will be Windows XP Server. This version is said to be still in primary betas. This one, is the one I want to put my hands on

.
Cheers,
El_Matador
PS: I hope to have helped you and not confussed you.