Ever since Heavensward, SMN has taken the path of not just summoning the Primals or their Egis, but channeling their power through their own body, hence the Dreadwyrm Trance that eventually became Summon Bahamut.
Basically the way it is now, we summon the primals, the actual primals, and it aligns our aether to their type, and we channel that type of aether for a short amount of time or until we summon the next primal.

Ever since FFIII, Summons have performed different roles depending on what the summon is. Or what job/character is performing the summoning.

FFXIV is just continuing the trend of summoning being different every entry.