I'm guessing that the reel you used the first time was a click and pawl, which basically means there's a gear inside of it with a metal piece that clicks (click) against the gear (pawl). I've circled the metal piece in red on the photo. The gear is on the back of the spool, so you can't see it here.
Your reel is a disk drag model so if you pull the spool off, you won't see any of the pieces you do in this picture, and therefore there's nothing to make the noise you heard on the other reel. Some reels have both the click and pawl and a disk drag, such as an Orvis Battenkill LA.
My passion for catching fish is eclipsed only by the fish's passion not to be caught.