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Games are now the biggest of all entertainment media and, like the other popular media, they use comic book iconography extensively in their layout and interaction.
The two did not start as a natural fit. Parlour games are self-contained and more about the possible and immediate, though you could extract some amusement from trying to get guests to guess that you're Light Lass.
Board games are a different matter. Before the advent of electronic games, these were the closest pattern to a typical comic book story. A card game has its rules and the queen of diamonds is an entity of a most prescribed kind. In either media, you have 'characters' and you can certainly replace chess pieces with characters from Deep Space Nine, but the movements and abilities are not affected by the character you choose.
Though there have been various board and card combinations, board games are not about gambling on an outcome but of pursuing a quest. A game as rudimentary as Snakes & Ladders is along this line. Ultimately they lead to the rise of Role Playing Games, or RPG, and the open-ended adventuring that would be increasingly dominant in console games as the technology developed.
Platform- What the game is going to work on. Anything that can play games is a possible platform(eg. "So what platforms will Splinter Cell be on?" "It will be on XBOX 360 and PC." So basically anything from PlayStations to PCs to Game Boys.
Platform Game- All games need a platform to process the data, so what is a platform game? Remember Mario? Banjo-Kazooie? Conker's Bad Fur Day? All of them fall in the genre of a platform game due- in the simplest terms possible- to a lot timing jumps between... platforms! So a platform game and a games platform are two completely different things.
Console- The same as platform bar one major difference. A console is something that's primary use is gaming. A PC will never be considered a console. A mobile phone is not a console. Everything else is a console, including handhelds.
No-one takes mobile gaming seriously. The pads are made for calling, the screens are small, and most importantly nobody makes good games for them(where's the market, yuppies who want a distraction while they wait five minutes for the bus?) Handheld gaming on the other hand is as big as gets. The Nintendo DS is by far the most popular console to date, and there are no signs of that changing.
Oh and you'll find RPGs are much, much more common on PC. The most dominant genres on consoles are FPS'(First-Person-Shooter) and Action games at the moment. In the past it was platfromers, and driving games have been popular forever. While there are many RPGs on consoles, I would never say they were dominant in any way. PCs are the birthplace and home to most RPGs and RTS'(Real-Time Strategy).
This has been changing quite fast recently due to the sheer popularity of consoles, which continues to rise dramatically(PCs... not so much).
Holy crap I'll stop there, I could go for days! Not sure what you're going for with this, but any questions you have I'll be happy to answer, I could have gone ten times deeper into most of the things above, but I don't want to kill you with boredom. So far though it's amazingly obvious you don't play games by reading that post.
Oh and 'computer games' is just another term for the medium(usually used by people who know nothing about video games), 'video games' is the common term.
[Johan v. 2008]