There are so many differences. First, the snooker table is much bigger than a pool table (12x6 feet). In snooker there are 15 red balls and six other-coloured balls. When you go to the table you first have to pot a red (1 point). Then you have to pot one of the other-coloured ones (they have points from 2-7). If you successfully pot one of those it is replaced on the table on it's spot (the reds stay down when sunk).
You then pot red/non-red until all the reds are down - and then you have to play the non-reds according to value, starting with yellow, ending with black.
Players like to go for the black inbetween the reds since it generates the most points. If you succeed in sinking 15 red with corresponding 15 black, and then sink yellow-green-brown-blue-pink-black you have achieved a "maximum break", ie 147 points. This happens very rarely, it is in fact quite amazing that it has happened two times so far in the world championships. To illustrate: The one who makes a "maximum" during the world championship receives £147,000 (of course they have to share it now since two different players made it).
http://en.wikipedia.org/wiki/Snooker