From an atheistic point of view death is nihilistic. The end of a being or entity. In Buddhism there are no beings, entities, or even objects. These are concepts. Reality is only moments of experience. Moments of seeing, hearing, smelling, tasting, touching, and thinking.
Nibbana is the cessation of experience. Since there is no entity or being that stops existing there is nothing that dies or is annihilated. There's just no more experience that arise.
It's a subtle difference but the main thing is the reference point: objects and entities vs moments of experience.