Yes, you're correct. Many researchers in the field prefer the phrasing 'human health', the consequence of which is human longevity.

Don't they go hand in hand?

Not necessarily. There are science fiction stories about extension of youth without extension of lifespan, and ancient myths about people cursed to live a long time without youth.

It's possible to imagine health-extending treaments (artificial joints and organs (heart), lung flushes) that don't extend lifespan). We already have treatments that can extend people's lives without health. (Unsuccessful chemotherapy, for one; insulin for type 2 diabetes mellitus, for another.)