Never is a negative time adverb meaning 'not at any time', but no/not (variant combining forms) is a much more versatile and important chunk of English. Not is just one of the forms it uses when it's a separate word, instead of existing combined in a compound or contraction.
It's the basic Negation marker in English. So it can be adjective and adverb, but mostly it's fused into phrases and contractions, of which never is one. Never is a contraction of no/not + ever, just like other contractions of no/not:
- never = not ever
- none = not one
- neither = not either
- nor = not or
- no way
- no one
There are corresponding contractions with the Negative Polarity Item any, like:
which are Negative Polarity Items, like ever.
Ever means what *anywhen would mean, if there were an English word *anywhen that was as commonly used as anywhere; in the same way, both of them means what *all two of them would mean, if that phrase weren't ungrammatical.
More important, as a Negative Polarity Item, ever can only occur within the scope of a Negative Trigger (or, as in never, bonded morphologically to its trigger).
Thus, ever is fine in these 3 sentences, with Negative Triggers (has)n't, few, and doubt,
- He hasn't ever seen it. ~ Few people have ever seen it. ~ I doubt he's ever seen it.
but it makes the corresponding affirmative sentences ungrammatical, though they're OK without ever:
- *He has ever seen it. ~ *A few people have ever seen it. ~ *I think he's ever seen it.