There are two ways to buy cryptocurrency. Through a broker — as a contract for difference (CFD), like in the simulator. Or on a crypto exchange — there you buy the coins themselves. But while the coins sit on the exchange, the exchange holds them: the coin is yours only as long as the exchange is honest and still standing. If it goes bankrupt, like the FTX exchange in 2022, you can lose the coins.
To keep coins yourself, you need your own wallet — an app or a small device that holds access to your coins. It comes with a secret phrase — 12 or 24 words. Whoever knows the phrase owns the coins. Like the key to a safe: lose it and you can't open it; hand it over and someone opens it without you.