What is the difference between a computer game and a video game

Computer games are video games. They're classified as PC games.

But i know you mean console games (ps3, 360, wii) vs. PC games, so I'll answer that.

PC games generally contain more content, come out at a lower price ($50) and can be modded, played online for free. But, you have to put a lot of $$$ into a PC to play the latest games. The PC is undoubtedly better looking and has better controls than console games, but consoles are cheaper by far, and the games are optimized to run on that console's hardware, so a steady framerate is present.

Console games are generally easier to play though, and more people do.