Coinbase wallet can connect to Coinbase.com. But some website doesn't use Coinbase wallet. Most websites use Meta Mask wallet. Which one is better Coinbase wallet vs Meta Mask wallet?
You can connect coinbase wallet to coinbase.com still you need to make on-chain transaction to move funds between two wallets. WHole meta mask wallet is used by most people for storing connects which connects to the decentralized exchanges. While coinbase don't support tokens or most of them so don't confuse these two wallets which are completely different types.