Like any other occupation, business or hobby, patch collecting has its own terminology. Long before digital cameras and scanners, if a collector was trading or selling a patch, he had to describe it.

Colors and sizes are easy, but when it comes to shapes other than square, oblong, or rectangular two phrases  were coined and stuck.

CHP shape and LASD shape.

 CHP of course stands for California Highway Patrol and LASD is Los Angeles County Sheriff Department. These two style have been copied by many other departments, and descriptions including  those styles are still often heard in the patch collector world.

In the 1960s "plastic back" patches became popular. The fabric of the uniform and the patches, being different, and shrank and wore differently, a few cleanings would end up making the patch wrinkle. Plastic coating on the back solved that.

Similar to plastic backing is "heat seal" backing.  This is almost indistinguishable from plastic backing until it is heated. This is used to apply patches to other fabrics by pressure and heat.

Mylar thread simulates bullion embroiderey, except it is a synthetic rather than a metal thread, although it looks metallic. Mylar is usually seen in silver and gold.

You will find much of this patch information and more in the book Pocket Guide to Collecting Badges & Patches.