Here's a simple question: Is 15-pound felt paper considered a vapor and moisture barrier, or a vapor and moisture retarder?

Retarder.

Ditto! It's a retarder. Now days, the NWFA and NOFMA have gotten away from the term "vapor barrier" and "moisture barrier". They prefer to use terms like diffuser, retarder, transmission reducer, etc.

O.k. then, a less simple question. What does NOFMA and NWFA consider the criteria for a vapor and moisture barrier? And what common product(s) is/are best to achieve these criteria?

They actually don't consider anything to be a moisture barrier. However, there are different ways of doing things depending on the circumstances. On concrete slabs, there are moisture control products made by Franklin, Taylor, Bostick's, Sika and others. One can use inexpensive vinyl as well. Or asphalt mastic and 15 lb. asphalt felt layered up. Over wood subfloors, the idea is to prevent moisture from entering the area below the subfloor in the first place by proper grading and drainage pipe. Then typically, covering the earth (if it's a crawl space) with 6 to 8 mil polyethylene. On top of the wood floor, NOFMA and the NWFA recommend 15 lb. asphalt felt. I use that on unfinished 3/4" flooring. On prefinished and thinner hardwoods, I prefer Aquabar "B" by Fortifiber. NONE of these systems are considered moisture barriers. As I said, that term isn't used so much today. It's about moisture CONTROL and vapor retarders.