There is nearly no part of the game that isn't changed.
1) Corruption doesnt' exist, at all. Every city is as productive as any other city. Having lots of cities, though, can crash your empire, as each city has upkeep, and each new city raises the upkeep on ALL your cities.
2) No governments. Instead, the effects you get from different governments in Civ III you get from different civics - switching civics takes a turn or two.
3) Worker actions and improvements - you get fewer workers, and there are many, many more things they can do. Decisions have long term implications (ie, if you want to go cottage based, you need to start pretty early)
4) Combat is really different - much more variety in what you can do, but also needs more planning. Units get bonuses vs other units.
5) Tech tree is pretty similar, but more decisions need to be made, to get military or to get worker actions or other things.
6) Religion. Totatlly different.
7) City specialization. In civ III, you could specialize somewhat - in Civ IV, it's almost a mandate - some cities may get all cottages and produce money/science, some may get nearly none and only produce military.
Maybe it's better to say what is the same....
each citizen requires 2 food? Sounds about it...