Coinbase wallet can connect to Coinbase.com. But some website doesn't use Coinbase wallet.
You can connect coinbase wallet to coinbase.com still you need to make on-chain transaction to move funds between two wallets.
Jawhead999 said otherwise but I would like to read this myself. I was browsing their Help page but I couldn't find what I was looking for. Can you drop me a link where I can read this Coinbase policy.
It honestly doesn't make any sense if you still have to pay transaction fees between custodial platforms owned by the same company. Why even bother?