You are right, that is not a Walnut (Juglans sp.). That is one of the Hickory group, of which there are several native to southern states that look a lot alike. Carya is the botanical name for the genus.
The nut/seed looks too small to be either Carya ovata (Shagbark Hickory) or Carya laciniosa (Shellbark Hickory), but it could be any one of 4 or 5 other species like Pignut, Mockernut, Bitternut, and others. Georgia is fertile ground for these kinds of trees.
You can try to photograph additional parts of the plant, to help others here try to identify it further. Some of these closely related trees are only separated by numbers of leaflets on their compound leaves, or a bit of difference in the dormant buds, or by hairiness (or lack of it) on various parts like petioles, rachis, petiolules, or veins on the undersides of the leaves.
Entertain us with your photographic prowess, and we can all learn something. Show us more of where this tree is growing, and tell us some of who it hangs out with (friends, associates, heirs, and assigns forever...).
