Well they're both strategy games.
The thing is the Civ is not an RTS. RTS = real time strategy.
Though I haven't actually played it, I'm under the impression that Civilization is a TURN-based strategy.
Typically, that means that you... take turns with your opponent.
I used to play Master of Orion II, and that was turn-based as well. So if it we my turn in that game, then I'd get a chance to give orders to each of my colonies as to what structures/ships I want them to build, and each item would take a specified number of turns to finish building. I could also order my ships to move, and how far they moved each turn would be determined by the engines on each ship.
Then you would get a turn, and a get a chance to do those same things.
So the main difference is that I get to take my time deciding what things I'm going to build, as opposed to REAL-TIME strategy, where if I take my sweet time making decisions, you're going to kill me before I get any defenses up.