I owned a mahog stoptail S and an SG not too far apart from each other. And no, aside from the fact that any two guitars will sound different regardless of model I think that in general these two will sound at least a little different because of the maple neck on the S versus mahog neck on the SG, and bolt-on vs. set neck construction. And then there's pickups, pots, etc...
The S is thinner, a bolt on, and has more wood routed out (in most cases), it's not quite as beefy as an SG, still a good guitar though. For example, mine has H/S/H config w/FR style trem. That's a lot of wood missing compared to the SG.
Great guitars, though. Not head heavy like some SG's, and not prone toward any neck/head damage either.
I've never played an S that sounds like an SG. The difference between the amount of wood and the difference in neck wood play a really big role. And like everyone else has said, 9 out of 10 SG's are going to be beefier than a S. Tone wise I've never played a S that I liked as much as an SG, but I love the ergonomics and playability of the S series.