When you call, the person on the phone types your order into the till and reads it back to you (sample). The kitchen printer by the pass prints the ticket a second later.
The ticket goes on the rail above the heat lamps. Anything you told us about allergies is printed in red at the bottom, so the cook who picks up your dish sees it first.
When every dish on the ticket is on the pass, it is packed, checked against the ticket once more and the ticket is folded into the bag. That is the paper you find on top.