This comes from Billy of the World Series of Beer Pong:
"Some suggest that the two are quite different, but those people are closed-minded. Beer pong, as best we know, originally started as a game in which paddles were used to hit a ball back and forth on a ping-pong table with one cup of beer on each end of the table.
Although rules vary, the general idea of this game was that if the cup was nicked, the team sipped the beer. If the ball went into the cup, the team drank the entire beer.
In more recent years (maybe since the early '80s), people began throwing ping-pong balls into cups (more than one) of beer. Some say this version of the game is called Beirut, not beer pong.
The truth is, however, an overwhelming majority of people in this country call the game of throwing a ball into multiple cups (not using paddles) "beer pong," not Beirut.
Therefore, the way I look at the two terms is as follows: "beer pong" may be played with paddles or without paddles; "Beirut" is a subset of beer pong and is played without paddles."
Thanks for the input, Billy!