I realize it's a matter of semantics. The practical difference may be non-extant. If you're on the fence on it, assume a "more like ____ than _____." Since it is a matter of semantics, I'm really interested if anyone would conceptualize different words for the pairing, or pairings.
Is despair the absence of hope?
Yes. Despair is the emotion of the lack of hope.
No. Despair is the presence of an emotion apart from (but contrasting to) hope.