Coinbase the exchange--the thing which involves a website--is a centralized pseudo-banking product where they actually own your money and you pray they still have it when you want access to it later. You use a username and a password to log in to this service which transacts on your behalf, and you talk to their customer support if you are locked out somehow.

Coinbase's wallet app is entirely different and largely unrelated: it is a program that manages a private key on your phone so you can directly access your funds and make transactions on the underlying decentralized infrastructure. If Coinbase goes out of business their wallet app would still function and no one has access to your money except you, using this key.