
What changes when you hold the keys
The coins are entries on the blockchain. A wallet holds the keys that can move them, and nothing else. Whoever has the keys owns the coins, in the only sense the network recognizes.

When you hold the keys, there’s no company between you and your money. Nobody can freeze your bitcoin or ether, or limit your withdrawals. Nobody can go bankrupt with your coins inside, or decide you’re no longer a customer.
The balance you see is what you have, with no promise attached. Stablecoins are different: the company that issues one can block its token.
When the Central Bank of Ireland warned people holding coins with unauthorized providers, its advice was to move them to an authorized provider “or to a self-hosted wallet.” A self-hosted wallet is a wallet whose keys you hold.