Like MrBaggins says, Civ2 is based on Civ1 and it's made by Sid Meier and Brian Reynolds, it's a really old game, it was released in 1995. It's the same type of game as the Call to Power series, but it looks and plays very differently (see
http://apolyton.net/civ2/ for more info):
Civ2 was probably one of the most popular PC games of all times, so obviously many games similar to it have been released. Alpha Centauri is one example and Civilization 3 (the official sequel to Civ2, released in 2001) another (both were incidentally developed by the same people who made Civ2).
The two Call to Power games (released in 1999 and 2000) are yet others examples of games inspired by Civ2, but they were made by very different people from a very different company. It can be slightly confusing that the first CtP game was officially called Civilization: Call to Power, but the Civilization prefix was only there to help sell the game to old Civ2 players, it doesn't mean CtP and Civ aren't very different games. For one thing, they are 4-5 years newer and have much more advanced graphics and the like, but many of the concepts in the game were also changed (opinions differ widely on whether the changes are for better or worse). But the basic game concepts are still the same as in Civ1 and Civ2 (replay history, build cities, research advances, create wonders, expand your empire, conquer your neighbours, rule the world, etc), so the CtP games (as well as SMAC) are often still regarded Civilization-type games (called that way because the original Civ1 basically defined the genre).
So the Civilization gaming world roughly looks like this:
Civilization 1: released in 1991, inspired dozens of other games and defined the 'Civilization-genre'.
Civilization 2: released in 1995, the official sequel of Civ1, it perfected the Civ concept and became one of the most popular PC games ever.
Civilization 3: released in 2001, the official sequel of Civ2, a much more modern game with many changes, but not necessarily a better game (it's not easy improving on (near-)perfection).
Alpha Centauri: releaed in 1999, a game similar to Civ2, but with much more modern graphics and a different setting (Alpha Centauri rather than Earth); gave Civ2 players something to play with until the release of Civ3.
Civilization: Call to Power: released in 1999, a game inspired by Civ2, but a very different game made by a very different company, which hoped people would regard it a sequel to Civ2 even though it's really unrelated.
Call to Power 2: released in 2000, a sequel to CtP1, which improved upon its predecessor, but it's still unrelated to Civ1/2/3 (the Civilization prefix had to be dropped due to legal issues). Of course, the people in this forum will say that CtP2 is the best game of them all, but beauty is in the eye of the beholder...
(There are some other games that are often also seen as falling in the 'Civilization genre' (such as Colonization, FreeCiv, Clash of Civilizations, etc) but they are all also similar yet unrelated games to Civ1/2/3, like CtP and SMAC)
Hope that helps...