Someone lacking in google-fu?
Just do a search using 'Bitcoin Proof of Work' or 'Bitcoin PoW' and you will get a ton of answers...
As for making money, mining and trading.
Mining is only if you have good rates for electricity and a place to house the very loud and hot miners. Trading is if you do not have that.
Also with Proof of Stake (Pos), staking is where you can make money out of it. Trading as well.
Obviously this isn't like mining where you need a device to stake, all you need is the wallet to stake. Users are even staking on exchanges like binance since they also offer to stake inside the exchanges. There are cons to staking on exchanges so you might just wanna check what are those try the google-fu.