If you are working with this specific profile, the "paper" involved typically serves one of these purposes:
In woodworking and architecture, (not wax paper) is commonly used to protect surfaces and tools when creating decorative profiles like a "bead and quirk". bead and quirk
For craft beads that might use similar terminology, parchment paper is the standard barrier to prevent sticking. If you are working with this specific profile,
Modern workshops use quirked beading bits to achieve the same rounded edge and recessed shadow line on table aprons or cabinet doors. bead and quirk
A simple, shop-made tool used to "scratch" the bead and quirk profile into wood, particularly useful for custom or curved work. Customer Questions & Answers - Amazon.com