Not = used to form or express a negative
It is not day; it is night
He is not clever.
Neither = determiner & pronoun not the one nor the other of two people or things; not either.
Neither day suits me for the appointment.
Neither cat is black.
• adverb 1 used before the first of two (or occasionally more) alternatives (the others being introduced by ‘nor’) to indicate that they are each untrue or each do not happen.
It is neither day nor night; it is evening.
He is neither clever nor stupid.
2 used to introduce a further negative statement.
He is not clever; neither is he stupid
It is not day; neither is it night.