Mining is voting weighted by wasted CPU power. Stake is voting weighted by wealth. That's all, really. Both are used to build decentralized networks, since the

Mining is voting weighted by wasted CPU power. Stake is voting weighted by wealth. That's all, really. Both are used to build decentralized networks, since they allow it to pick a random participant to order the previous X transactions (aka block), without being susceptible to sybil attacks. PoS is much less energy-hungry than PoW, but it has a problem: how do you distribute money fairly, to begin with? Which is why Ethereum started with a few years of PoW to only then shift to PoS. Pretty clever IMO.