Honestly, it could be both.
It's schizophrenia in that it's your mind, but you're not the individual speaking. However, it could also be paranoia if you are afraid of this other "you" and what it does while the "real you" isn't aware of things. It all depends on the individual in question.
In the case of Brain Damage from Dark Side of the Moon, I'd have to say it's both. The character in the song (Waters?) is most likely schitzo, but from the tone of the song he is afraid of this other him.
But remember: IANAP. Take what I say with a grain of salt.