Which term is more likely to have been used in Georgia around 1893? I found a British website which explains the origin of the modern game known as American pool (http://www.tradgames.org.uk/games/Pool.htm.) They say that all the predecessor of all modern "pocket billiards" games was American fifteen-ball pool or "sixty-one pool." They also say that "continuous" pool (the same as fifteen-ball pool but with a different scoring system) replaced fifteen-ball pool as the championship game in 1888. What I am not sure of, however, is if the generic term for these games was "billiards," "pool," or something else in the 1890s American South.
The South is a pretty big place, but—at least in Virginia in the 1890s—billiards, pocket billiards, and pool were all commonly enough played (and gambled on) to draw the baleful eye of the state legislature. Here is the first half of section 2835 of chapter 228 of the state code of Virginia "relating to dealings with students and gaming" (approved February 8, 1898):
I wonder how frequently the authorized officers of the University of Virginia gave prior written permission to students to borrow money to play billiards with.