there are three, softfork, hardfork and fork a coin. softfork and hardfork has been explain above.
fork a coin means you clone a coin and create a new coin with new genesis and blockchain. you need at least 2 nodes in order to make your new coin/blockchain live.
That's the same as the software fork i explained above, Litecoin being the first. Bitcoin is free open source software, anyone can take it, change it, and start it again from zero. That is not really a "coin fork" (that term would actually be misleading). Of course forking the bitcoin software usually produces a different coin...