Regular matboard is not acid free but it's acid neutralized, meaning it's far lower in acid than something like chipboard.
Rag is reference to cotton rags, meaning the board contains cotton fiber. "Rag" generally means the core of the matboard is cotton or contains cotton and is acid free, "Museum rag" (4 or 8 ply) is thicker, all cotton, and also acid free.
It's the wood pulp in non-cotton board that breaks down into acid (lingin, I think is the culprit) and yellows. The discoloration is actually a chemical burn.
I agree with Michelle, the acrylic from FAA is not UV. UV acrylic has a slightly stronger surface reflection (IMO, maybe I'm imagining it but I don't like it) and it's way more expensive.
It's not pointless to print on acid free and then frame with regular materials. The acid free paper will hold the ink color longest, regardless of what it's up against - it provides kind of a barrier itself. Mats nowadays are acid neutralized and will last longer than those of even 15 years ago. I agree if you want a completely archival frame job, you'll need to hinge tape the art (I think the art standard bigwigs consider dry mounting to be destructive because it's irreversible), and you want your image to be completely air tight, which doesn't happen with regular every day framing, regardless of what materials you choose.
True archival sounds like a good goal, but you can buy a $400 print and spend $1400 or more easy having it truly archivally framed.
So choose the best materials you can afford, is the short story. Rag mats will stay white longer than standard matboard and won't yellow. Regular mats may discolor after many years. Make sure the paper dust cover is well attached on the back and keep your framed artwork out of direct sunlight no matter what glazing you choose.