"Ah, you're going with the Angel and Angelus are two different people thing."

That, or they're at least two separate sides of a split personality (Jekyll/Hyde style), if the mental struggle in "Orpheus" in any indication. There's also the fact that when knowledge of the Beast was erased, Angelus was unaffected due to being absent from reality when the spell was cast.

This contrasts distinctly with Spike, whose post-ensoulment persona is the same as before except with a(sometimes humorously denied) conscience.