Adrenaline doesn't know what it's for. It widens the pupils, sends blood to the big muscles, speeds everything up. Whether that becomes terror or thrill depends largely on what you happen to be looking at while it happens. Which is why the body before a first date and the body before bad news can feel so nearly identical. Same shaking hands, same shallow breath.
None of this makes fear trivial. It does mean the sensation is fuel rather than a verdict — the body handing you more than usual, in a hurry, in case you need it. Usually you do. Just not for running.