You are right that there’s a seller and a buyer in a stock transaction.
You are incorrect that both parties think that they are making money. Most of the time, it’s just a trade where the value of the money and the stock are the same. They’re just trading 1-for-1 two things of equal value (at the time of the transaction). Nobody’s making money except for the broker (ETrade, or whoever) that’s charging both of you a small fee to document the trade and keep your account records.
The value of things goes up and down, in part because someone does / makes something useful, and in part because someone thinks that something someone did / made is useful. The value of money and stocks goes up and down. They’re alike in that way, but money is special in that you can use it to pay for things. Stocks, on the other hand, represent a share of the value of something — like a company; you can’t buy stuff with it, but you can trade it, and even trade it for money.
The important thing to realize is that there’s not a fixed amount of “value” out there. It’s not like a bag of candy where if I take one there’s one less for everyone else. It’s more like a candy factory where I own 10% of the candy in the bowl and more candy is constantly going in and out.
You make money in stocks by trading money for a slice of the company. You pay a price based on how much that company seems to be worth. You hope the company does / makes stuff so that it grows, and your piece with it. Then you can trade that bigger and more valuable piece for money again — more than you started with. There’s nothing lost here. People lose money when they buy a share of something that loses value over time — perhaps people stop buying the company’s things, maybe they couldn’t get the materials they need, whatever… If the value goes down compared to when you bought it, and you trade it for money, you’ll get less than you had before — a loss.
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