Essentially the aim is the same in the game. The weapons are the same, the engine is updated and if you configure the servers properly the hit reg is as good too. The game works slightly differently though due to small changes valve made in the recoil system etc, meaning that if you are good at cs1.6 you are not necessarily as good at css (and the other way round), which of course the pros didn't like. Also lots of servers are misconfigured so hit registration can be quite bad on source in these cases, whilst 1.6 in more forgiving in that respect.
Mainly it's the same game, but because "pros" don't like dropping back to being bad at the game due to the minor differences, it's supposedly different. (Same thing in CZ, if you are good at 1.6 you aren't necessarily good at that either.)