Great question! This one had me scratching my head for several years and delayed my getting into Bitcoin, so I'll see if you I can save you the trouble and confusion in this post.

First, this episode of the Bitcoin Dad Pod is what finally made it click for me, I would highly recommend giving it a listen.

TLDR: Power vs coins is the wrong way to frame it. In PoW you trust the constraints of thermodynamics and probability. In PoS you trust the honor of those with the money.

Full Explaination: Essentially, the idea of PoW being who has more power and PoS being who has more coins is an oversimplification of how it functions, although obviously no one blames you for the confusion, as it's an easy mistake. Although in PoW you can 51% with enough ASICs and in PoS you can 51% with enough coins, the true difference exists in what happens while each protocol is operating normally, ie, when no 51% attack is being preformed.

In PoW we achieve decentralization by requiring every miner to put a hash with a certain number of zeros on each block. This is a requirement enforced by the nodes, ensuring that a certain amount of work must be put in to count a block. If a block does not meet these requirements then the nodes will reject it and wait for another miner to broadcast a block.

In PoS, the nodes don't have any such requirement. All that the network asks of stakers is that they lock up a certain amount of their coins and continue to produce blocks when it is their turn. Essentially, you trust that those with the money to stake coins have an incentive to not overtake the network, censor transactions, etc.

Thus, we have a distinct disconnect. PoW has distinct requirements imposed by the nodes to ensure decentralization and non-censorship, while PoS nodes set no requirements. Granted, you coins can get slashed under PoS, but that is only in the case where either your staking node goes offline for too long, or if you try to send out two blocks at the same time. Neither of those ensure decentralization in the same manner as PoW though.

PoW vs PoS is a very complex topic though, and I would encourage you to research it more. But at the end of the day, they are dramatically different protocols, making it so that "PoS is PoW but coins instead of power" is somewhat of a mischaracterization.

This post in meme form: