OK so after reading everyones replies this is what I get out. At the point where I buy and keep them at Coinbase or send them to another Coinbase account the keys are never involved. But if I decide to send the coins to another exchange, then the actual keys are in fact sent at that point? So that means if somebody were to hack into my account and transfer the coins to their account, then at that point the keys ARE sent along with it?
There are no "my keys". The keys are Coinbase's keys. You have an
account at Coinbase with a balance.
Keys are not sent, but are
used to send.
However, moving bitcoins between Coinbase accounts consists solely of changing the balances of the accounts. Nothing is actually moved or sent.
Perhaps you believe that each bitcoin has a private key. That is not how it works. In simplest terms, an address holds bitcoins and an address has a private key.