Multiple Personality Disorder and Schizophrenia are not the same thing. They are in the same family of mental disorders, this being dissociative disorders.
Multiple personality disorder is where one person reacts differently in the same situation because it's apparently several people, or several very prominent aspects of that one person, inside the head. Not all the personalties have access to all the memories. You may have done something totally out of character and then deny it when you're back in your own head.
Schizophrenia is where somebody hears voices that aren't there, sees things that aren't there, can't interpret figurative things as being figurative, has delusions, and a generally disordered mind. Perception of reality is totally wacked. Messages from God, great big shadowy conspiracies out to get them, et cetera and so forth.
In other words, the multiple personality person percieves the inside of their head to be the wacked part, or else has no clue what the hell's going on, and there are a lot of them. (Two can be a crowd.) The schizophrenic person sees that the rest of the world is perhaps more wacked than it actually is, and has perceptual problems.