What's the difference between buying a "PC game" and a "PC code"?

"PC Code" or "Key" refers to a product key that can be used to activate a game on a download platform, such as Steam (the big one), Origin (EA), uPlay (Ubisoft) or GOG. Once activated, you can download the game through this platform. Typically, this platform will also keep your game up to date.

If a product is sold as "PC Code", you will (probably) not get a physical disc copy. The article description should note which platform the key can be used on. Note that Far Cry 3 always requires uPlay, even when buying a steam key (launching the game will launch the game through uPlay).

A word of warning

Be very careful who you buy product keys from. Not all key sellers are legitimate, and using a fraudulent key (such as one bought with a stolen credit card) may result in the platform owner removing the game from your library. Take a look at this reddit post for more information about key resellers.

Speaking of Far Cry 3 specifically:

PC Standard is the physical disc. You will still need Uplay to activate it.

PC Download Standard and PC Download Deluxe are codes to be redeemed on Uplay.

PC Download Standard - Steam DRM and PC Download Deluxe - Steam DRM are codes to be redeemed on Steam, but this is just a semi-redeem, Steam will launch Uplay when you launch FC3, and it will ask you to redeem the code again the first time you launch. After that it launches Uplay (updates it) and then the game automatically.

So in conclusion: You always need Uplay.