Civ 3 Complete (C3C) contains and installs are three versions of Civ 3, all three fully patched; vanilla (1.29), Play the World (1.27) and Conquests (1.22).
Once installed, C3C will default to play Conquests, though the other two versions are installed also. But you will need to create a new shortcut to start them or else navigate to the respective folder and start the .exe manually.
When C3C is installed, both Play the World and Conquests are installed in their own folders inside the main Civ 3 folder.