The difference is that the word "disease" is something that at least theoretically can be cured. Aging does not have that implication. It follows then that if you say "Aging is a Disease", you're effectively saying that immortality is theoretically achievable. That's what makes the claim so uncomfortable.
Nowhere does the definition of disease imply that. There are many diseases today that are patently incurable.
Aging, like cancer, is multifaceted. There are many low hanging fruit that we can begin to tackle now.
> you're effectively saying that immortality is theoretically achievable.
I'm not saying anything about immortality. But I don't see how a 100, 120 year average lifespan with expanded quality of life isn't achievable.