During the great depression, the "pool halls" were basically gambling establishments where you could place off track bets and wait to hear the ticker or runners come back with results. As part of the business, billiard tables were installed so the normal patrons would stick around and bet more. These began being referred to as pool tables.
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In layman's terms: Nothing. It depends on who you are talking to, and where you are having the conversation more than any 'rule' that says this or that. There are 2 different types of tables, dependent more on the game you are playing as to any 'term', but terms have developed needless to say. Please note that all of these tables use the standard 2:1 ratio in size. Those two tables are: A "Carom" table is a pocket-less table that is always 2.84m X 1.42m (5f X 10f) and uses a 'heated slate'. This table is used (normally) for four different types of games under the general label of "carambole billiards" which are very close the the popularized "Snooker" type games. A "Pool Table" or "Billiards" table is a table with pockets that come in a variety of sizes ranging from 6 feet to 12 feet. General acceptance says that tables at or under 8 feet are for "pool" and tables larger than that is for "snooker." Although all sides will argue exceptions to that rule, and each of those exceptions are acceptable. IE: When in Rome...... The term "Billiards" encompass the 'whole' of this type of game.
If you were to visit a "Billiards" store you would find BOTH types of tables in all those respective sizes.
If you were to visit a "Snooker" store you would most likely not find tables under 9 feet, or pocketless tables. In Closing: You will find (and I'm sure some may comment here) that you "Swim in a Pool" and "Play Billiards" if you play in a pool it is called water-volleyball or something. People who love the game (games) for what they are will not get into those arguments; it is all about the game not the people or terms.
(I say bugger those terms, I'm all about the game(s))