I’ve been studying hard wallets and wrote what I have learned. I would appreciate corrections if I was inaccurate, pls.

Every time you buy Bitcoin, a key is generated and stored by the exchange you use. A hard wallet allows you to custody that key, granting access to your bitcoins on the blockchain.

With a hard wallet, you avoid the risk of the exchange collapsing and taking your keys with it, as seen with FTX, one of the largest crypto exchanges globally.

The words or seeds are associated with your hard wallet and serve as a means to recover it in case of loss, theft, or damage.

In essence, when you keep your crypto assets on an exchange, they aren’t truly yours but rather belong to the exchange that holds custody of your keys. With a hard wallet, these crypto assets are genuinely yours, and no one but you has control over them.