Most trios do not fit the profile of a “true” trio exactly. The musical texture may fit the description, but the context will demand that some part(s) be registered more prominently than others.
This idea of prominence of a part and unequal volume of the parts moves in the direction of solo and accompaniment registration. In fact, the exact point at which trio registration becomes three-part solo and accompaniment registration cannot be precisely pinpointed.
Since the usual trio involves some element of prominence in parts, perhaps trio registration can best be understood when compared to solo and accompaniment registration.