And aedra can only create things that don't exist, daedra can only change things that already exist.
That is just mythcial sueprstition. The Aedra are bound by the creation of the world, but nontheless there are no inherent differences between Aedra and Daedra. Both are et'ada, spirits/gods (of which there is no difference). Before the creation of the world, the spirits drifted into and out of existance in the Aurbis, the grey maybe between the universes two constant forces, Anu and Padomay, and there was not yet a split between them. Before the cretaion of the world there were no Daedra or Aedra, merely et'ada.
Those spirits that took part in the creation of the world were then called Aedra. Those who did not and created own realms in Oblivion were called Daedra. And then there are those who fled creation or were not part of the wheel (Mundus [incl. Nirn]+Oblivion+Aetherius) toi begin with. Those are sometimes called Mnemoli or STar Orphans.
Thats the only difference between Aedra and Daedra: The Aedra particpated in world creation, hence "Our ancestors". The Daedra did not, hence "not our ancestors" (the Dunmer turned this around, of course, but they meant a mythical-spirtual meaning of ancestors). Of the Aedra, some became the Eight Divines, some became the Earth Bones (the personified laws of nature, sometimes worshipped as gods, too) and some merely became mortal, being the true ancestros of men and mer (at least, thats the Elven view on it, but even for the men there doesnt seem to be a true "gods create humans" myth, so the Elven view seems correct to me).
Sometimes, all et'ada aligned with Anu are called Aedra, and all et'ada aligned with Padomay are called Daedra. Oblivion, as meta-realm, surely is Padomay-aligned, and so seem to be all Daedric Princes. But Lorkhan, OTOH, was Padomay-aligned, yet the central character in the creation of the world, so must be counted as Aedroth.
sooo basically exact opposites
with very similar names??
No, tehre ar eno exact opposites. There is no polarity - Aedra are not Angels and Daedra not demons. Only a technical definition split going back to the creation of the world.