Owning crypto means controlling a private key. A wallet doesn't 'store' coins so much as store that key — and whoever holds the key controls the funds. Understanding this is the whole game.
Custodial wallets — like the balance on an exchange — hold the key for you. Convenient, but you're trusting a third party. Self-custody wallets put the key in your hands, giving you full control and full responsibility.
The famous phrase is 'not your keys, not your coins.' For small, active balances, custodial is fine. For amounts you'd hate to lose, learn self-custody: back up your recovery phrase offline, and never share it with anyone, ever.