Proof Of Work (POW): This protocol works in order to find a solution to difficult mathematical problems, which are getting verified afterwards. All the work is rewarded. For example, Bitcoin, Litecoin, Doge are coins that belong to this category.
Proof Of Stake (POS): With this protocol, only the one who already has coins is rewarded. The reward is proportional to the number of coins, rather than work-related, and so the investment is actually rewarded rather than the work. Among others, this category includes Clams, Black Coin, Hyperstake.