Acapella and Barbershop singing are very similar and probably fall in the same catagory especially in that they are both, well, acapella. Gospel tends to fall in that arena as well although I'm not a fan.
The major difference would be that there are acually "Barbershop Chords". A true barbershop arrangement is said to consist of at least 35% barbershop chords...
The most amazing thing about it to me is to hear for voices ring a perfect chord. Four individuals using their voices to make a sound (or chord) that is otherwise made by four strings of a guitar, or piano, or {insert instrument here}.
