I have been told that my oak trees are white oak and live oak.
After reading your post I decided to look the trees up to ID them.
Both trees give acorn every year. I get two different shaped acorns. Both trees have a similar looking leaf, except one has leaves all winter so it is a live oak.
This appears to be the one that loses its leaves:
Mexican white oak (Quercus polymorpha)
https://gardenerspath.com/plants/landscape-trees/mexican-white-oak/
I will let you do the research to prove that it gives acorns every year. I could not find that information.