If you personally hold the private keys needed to spend the BTC then it is a wallet and you own the BTC.
If someone else holds the private keys then it is an account, you do not own the BTC, in fact you have lent your BTC to the person/entity that has the private keys. They have given you an "IOU" in place of your BTC and you have to trust that when it comes time to spend the BTC they will honor the IOU and give your BTC back to you.
Now given these definitions is coinbase a wallet or an account? I am not familiar with coinbase, have never used it and I am curious.