The original Counter-Strike(or Counter-Strike 1.6) is basically an old version of Counter Strike: Source. It was originally a mod from the original Half Life(it was referred to as "Half-Life: Counter-Strike at the time), which used the GoldSrc(or GoldSource) engine, a heavily modified Quake engine. They updated the engine and renamed it to Source in 2004, which came with new releases of Team Fortress 2, Counter-Strike: Source, Day of Defeat: Source, and Half Life 2, all seperate games.

Counter Strike: Condition Zero, was basically the same as the original but included a Singleplayer mode.

Counter Strike: Source, is and updated remake version of the original with a new engine, new graphics, etc.

Counter Strike: Global Offensive is another updated remake using and updated version of the Source Engine with new graphics. This time it has New weapons, maps, characters, guns, and gamemodes. It's the first Counter-Strike to support Cross-Platform gameplay.

3rd party Counter-Strike games:

Counter-Strike: Neo was a Japanese Arcade version of the original Counter-Strike. It was developed by Namco and runs on a Linux system.

Counter-Strike: Online is a free version of the Original developed by Nexon of South Korea. It aims towards Asian gamers. It has new gamemodes such as zombies.

Credit to Wikipedia