There's an opening, where there are a few tried-and-true, well studied strategies, and the goal is to claim territory.

Then there's a mid-game, where all available land is claimed, and competing players start trying to steal territory from each other, and capturing the others pieces (or cities).

I can't seem to find a parallel in the end game though, it doesn't require nearly as much planning and cunning in Civ to finish of a wounded opponent as it is in chess.