the main difference is time rate. and how cool it looks. all a TBS does is this:
click..... click..... click.... ooh, a ship moved!.... click.... wow, it rolled 2 damage!
in RTS, you can see ships all moving together, and even experience the joy of a good ol' fashun'd civil wah voll'y that decimates the opposing fleet. in my experience, a TBS doesn't really give that good of graphics, or of an experience. you don't get into the feel of the game, because you are always interupted by the turn changes. in an RTS, you can begin a project, skip on over to a fleet, tell them to obliterate something, go back to your project, tell them to obliterate the fleet that just foolishly tried to make a run past yours, jump back, jump to the battle again, etc. TBS gamers can't deal with pressure, because they refuse to admit time as a factor. in an RTS, you have the quick snap decisions like:
Boom, go there. boom, kill that. boom, build this. boom, go to this city. etc. its one after another after another. there is no waiting for the other person, or sitting around to make up your mind. you have to think on your feet.
A good RTS game to try: Age of Empires 2: Age of Kings of Sins of a Solar Empire. there is a number 3 in the AOE series, but only most people like it(even though I do) and number 2 is a general kick a$$ game. my fav civ is the vikings and the byzantines (one for land maps, the other for sea). It really capture the true enjoyment of the game.
also, try Joan of Ark's campaign - its a good starter after going through the tutorial.