I don't know if I'd call them "clips". It's more like the tray has slightly raised pockets around the rim of the disk drawer that keep the disc from sliding around too much once it's placed in the center when the tray is in motion.
They are however, not all created equally.
For example, in my MDD, the Pioneer 116 DVD drive has raised "lips" around the entire perimeter of the disc tray recess that can and do keep the disk upright pretty reliably. The disc slides downwards a tiny bit when placed in the tray and is cradled by a good 120° or so of "lip" around the "bottom" - enough to keep it there when the tray starts to move.
The Lite-On CD drive right below it however, has only 4 little tiny "nubs" placed every 90° that barely work at all when used vertically. The inertia of the disc itself makes it slide backwards and out from under the "front" innermost one when the drawer starts to close sometimes causing it to fall and jam up in the mechanism - enough so that I absolutely have to keep a finger on the disk for a second as the drawer accelerates. It also causes the disc to fall out entirely when opening if I don't have a hand there to catch it. It's an annoyance (or rather would be) that shows me they really didn't expect the drive to be installed sideways when they designed the drawer mold.