For Ethereum there are really two different implementations of PoS.
FFG (Friendly Finality Gadget): This is what people will refer to as hybrid PoW/PoS. Everything works the same way it does now, with miners mining blocks, but there will also be validators that vote on what block to finalize. Finalizing is an addition to the longest chain fork-choice rule where nodes refuse to revert a finalized block, meaning it's impossible for a 51% attack to undo more than x blocks (an epoch). More reading can be found here for basics and here for economics
TFG (The friendly GHOST): This is what people will talk about when they talk about full PoS, so it isn't overlaid on top of mining like FFG is. More reading can be found here and here