PoW coins future is limited to max 5 years for me. All going to turn PoS and this means less energy and a green world.
I think PoW coins will be around a lot longer than 5 years. But, I will agree they are going to phase out "soon."
But to reiterate for the OP --
PoW = Proof of Work. PoW is traditional crypto mining. Using hardware and electricity to provide solutions to work toward solving a block. When a block is solved a reward is granted to the miner(s).
PoS = Proof of Stake. This is when you have a number of coins that you are willing to "freeze" (can't be immediately traded) to support the network/project. PoS is done in many different ways. Sometimes it is through pool leasing and sometimes it is done simply by holding coins in an unlocked (for staking) wallet. You essentially get a small reward for providing assurance that you won't dump all your coins and for using your network (or pool's network) to assist with blockchain transactions -- the amount of coins you or your pool has increases it's weight (likelihood for rewards) and potential reward size. In short, think of this as bank interest for blockchains. The more money you have in savings, the more interest you receive from the bank each month/year.
PoC = Proof of Concept. It is very uncommon to see any crypto using PoC. I believe the general idea is that you need to prove your ability to mine with PoW or to stake a substantial supply of coins with PoS, but don't actually have to mine or stake anything (yet). I haven't participated in any PoC based projects, but I believe this would be something they might implement in early stages of development or before a blockchain transitions from PoW to PoS.
