In a few words, the main differences between CTP and Civ 3 are:
- no workers in CTP, but you decide how much you give each turn for public works (and then spend this money to buy roads, farms, advanced mines, etc...), the cost depending on the sophistication of the building and the site chosen.
- possibility of underwater and space cities
- within armies, you can have long range units and close combat units: when the armies fight, first the artillery (when available) fires, then the troops attack the injured enemies (because of the "bombing"). That is not the case in Civ III: each unit in the army attacks, and when it is badly injured the following continues the battle. Therefore they are not used according to their specific abilities...
- piracy is possible on commercial routes
- no special resources like Civ III
- no cultural "capture" of the other players' cities (but your territory has borders similar to the Civ III cultural borders)
- spies do exist in CTP (but have the same lack of success as in Civ III!)
- of course, different units, improvements, advances, wonders
- more governments