Correct, but there is a key similarity.
What (well, one of the things) FTX was doing was taking money then not buying the crypto. So you give them $100 to buy bitcoins, they were keeping the $100 and on paper you'd "have" $100 in bitcoins. If bitcoins went up 10% they'd eat a 10% loss. If bitcoins went down 10% they'd pocket the 10% you lost if you "sold."
Now, that's bad, but it's not the root of the problem. Your $100, plus everyone else's $100 which actually added up to a significant amount, should have impacted the price of bitcoins. Higher demand should drive the price up, right? Except there isn't higher demand, because the bitcoins never actually got bought.
Brokerages are doing the same thing with stocks. You, the retail investor, want to buy a stock. They think it'll go down. They effectively create a synthetic share and "sell you the stock" except you don't really have the stock. This is called a naked short, and it dilutes the value of the stock. The buy should push the price up, but it doesn't. It's possible to buy more shares of a stock than actually exist. It's manipulative and it's bad.