There are several types of live oaks from Escarpment Live Oaks to Coastal Live Oaks. I have both kinds.

But, and I could be wrong, that does not look like a live oak to me.

I have some oaks that are about the same size as the small picture that you posted. They did come from acorns also, so I am sure that they are oaks. It would be interesting to get these trees identified.



This is one type of live oak, I believe the Escarpment Live Oak.



The Coastal Live Oak has shorter, rounder leaves.

The tree the acorns came from looks like willow oak, but the young seedling does not. Problem is that the acorns cross breed so bably. Grow it into a larger plant and let's see what develops.