What are the Standard Terms Used to Describe Liquid Viscosity in Cooking?
The one I hear most often in professional kitchens is nappe, which is the "coat the back of a spoon" test. That is the general starting point for an average sauce that you can use in a wide variety of dishes; it is thick enough to cling to food without being stodgy.

Beyond that, I'm not familiar with other standard professional terms specifically for viscocity. Usually just thin, thick, stiff and so forth. Sometimes it is useful to talk in terms of percent reduction, as in "add 2 cups of wine and simmer until reduced by half", although in many cases this is done more by eyeball than with precision.