is a guy. Eminem
is the name he uses as a rapper. This is all perfectly simple.
Slim Shady is a persona created and used by Eminem.
The use of this alter-ego allows him express views, which would perhaps prove unacceptable to the public, while keeping a distance between himself and those views. It is an extra layer behind which he can hide. No matter what slanderous, bigotted, homophobic, sexist lyrics he raps it is possible for him to claim:
it's not me, fools. I'm not saying these things, it's Slim Shady. What are you, stupid?
In fact, Eminem has another persona, Ken Kaniff, which he uses to express homosexual thoughts that Slim Shady ridicules. There is an interesting relationship between Eminem and Ken Kaniff, and one which a psychologist - (I am not a psychologist) - could write many essays. IMHO, Ken Kaniffe is a useful release mechanism by which Eminem can relieve some of the pressure of a repressed homosexuality. In my limited experience of outrageous homophobes at least some element of self-hating homosexuality is usually present.
While I like Eminem's music, and find some of the songs on both albums really contagious, I couldn't really call myself a fan. Listening to Slim Shady songs is a bit like turning to see a trainwreck, or playing Soldier of Fortune. You know you shouldn't. You know it's probably bad for you, but you can't tear yourself away.