This "coin" stuff may be confusing if you are not familiar with algorithms and data structures. Let me explain what I know so far —
There are many, many coins. People like to trade them, not unlike stocks or Pokémon cards. People also mine them, using their home computers or specialized hardware.
Coins are stored in wallets which can be hosted online, on your local computer, or on a sheet of paper.
It is hard to mine a coin on your own, and is like gambling, so people usually opt to join a pool (which typically use the stratum protocol to coordinate) — this rewards you for your work, even if you didn't find anything because you helped contribute with thousands of other people, some of whom did find blocks. The blocks are then split up, based on the pool's rules.
Some people rent hashing power from farms and either play the "blockchain lottery", trying to find blocks of coins on their own, or they point the farm at a pool, like a typical home miner — except they have a tremendously high amount of computational power available to them, if they're willing to pay for it.
Hope that helps clear things up.