Fagaceae, Castanea, pumila
Fagaceae, Quercus, laevis
Fagaceae, Quercus, margaretta
Fagaceae, Quercus, marilandica
Fagaceae, Quercus, michauxii
Fagaceae, Quercus, nigra: this is the very common water-oak, and probably one of the 2 you are asking about. It has lobed teardrop shaped leaves in clusters with angled buds. Leaves are palmately compound. The trunks are ridged vertically, that is, it looks as though someone has taken a regular tree trunk, then glued more smaller straight tree trunks to it vertically all the way around the circumference, and finally covered them with bark.
Fagaceae, Quercus, pumila
Fagaceae, Quercus, virginiana: the very famous live oaks, probably the other you are looking for. Leaves are ellypticle, have revolute edges, clustered buds, have small tight acorns, are evergreen and sporadically drop. Also has heavy bark.

Another common tree to the area I want to include is the gum tree. I like them because they were in a girl-scout song I sang when I was a child; they are characterized by a leaf with five points, and often have prickly brown gum balls on the ground underneath. Also, I love them because of their scientific name:

Hamamelidaceae, Liquidambar, styraciflua

Pronounced

Huh, mam (a as in apple) muh lee day cee eee, Liquid Ambar, stie ra (as in apple) suh flu uh

Uh as in duh! And stie as in pie. Say it a couple of times. It’s fun.

You made my day arauquoia!

Aurelia

As the poster was asking about 2 types of live oak common to the area, and as far as I know only virginiana is the the true live oak, then I assume they actually want the 2 commomly know local oak trees, live and water oak. The rest of the list just shows the diversity for the area. A lot of people call any oak tree in the SE a "live oak."

Laurel Oak is commonly mistaken for Live oak and people in the area are forever calling it Water Oak, though the true Quercus nigra very obvious leaf, acorn, bark, and form differences. But it doesn't belong to the live oak group of oaks.

http://www.sfrc.ufl.edu/Extension/img/for51f12.jpg

Q.fusiformis, the Texas or Escarpment Live Oak, while native to TX, OK, & Mexico, has been planted well outside its native range, and may be the best bet for those of us in the frigid northland(zone 6) who want a live oak.

Boynton oak(Q.boyntonii) and Chapman oak(Q.chapmanii)are two other small, shrubby white oak species, though relatively rare, which may be encountered in the Coastal Plains areas as evergreen to subevergreen trees, with Boynton only being native to AL & TX, and Chapman being most common in FL.