For birds, we generally use the term adult to refer to the definitive plumages, both breeding and non-breeding plumages. In other words, the point at which the plumage doesn’t really change from year to year. That doesn’t always refer to the ability to breed - Bald Eagles, for example, take 5 years to reach adult plumage, although they can breed by their third year. (Most don’t get the chance, of course.)
It gets more complicated with some species, like Snail Kites (the females, at least) and the large albatrosses, where their plumage can change from year to year for many years.
In many cases, distinguishing adult birds from young ones is quite tricky, requiring a close look at the wing coverts, etc.