For some technical info on TCAS this is a great page
http://www.aerowinx.com/html/tcas.html
As for mode C and mode S tranponders I believe, although I'm open to correction by those who know a hell of a lot more about this topic than I do, one of the fundamental differences between the two is that a unique code will be assigned to a particular aircraft and it will stay with that aircraft for its life, or until the next best thing after mode S arrives, so ATC can ID a particular a/c. Hope this is of some use.