Proof of Work is a classical mining (if we not mention real miners working under the earth surface etc.) where one earns his coins as many as more power his ASICs are. They do not need to make other investments besides of eqipment.
Proof of Stake "miners" do not need to have any ASICs but they do need to buy a power server or a computer and they have to stake some amount of those coins they are going to get in future, it is kind of pledge or deposit. Actually they get some percent by checking and validating blocks from those chains or part of chains they responsible for.