Those are the magic words to an antique vehicle restorer, the words that put a twinkle in the eye and elasticity in a wallet.
OEM is Original Equipment (by the) Manufacturer, and NOS is New Old Stock. OEM just means that you can go out and buy a piece for your 2002 Corolla from the Toyota place, or from Bob's Diskount Auto Barn. It gets tougher as the vehicle gets older, because the automotive industry is directed by law to keep parts in stock for their vehicles for only ten years after that model is discontinued.
That's where NOS comes in. NOS is when Joe Bob is tearing down his Grandpa's old barn and finds out that Grandpa once stole an entire boxcar full of auto parts destined for a NAPA outlet in Marietta, and never got around to selling it. It's all new parts for 1942-1945 Studebaker sedans, and worth a mint, so Joe Bob goes and gets himself an eBay account and goes to town selling original NOS Studebaker parts.
Joe Bob is the sort of guy who can get rich over someone else's obsession.
See, the meat of the pudding is that NOS fits. Perfectly, usually, or as perfectly as any part ever fits any vehicle, because it was made from the original tools and dies from the manufacturing plant. Therefore there's a minimum of cutting, hammering and cursing when installing these parts.
So then comes the "Reproduction" part. See, if you're lucky, some manufacturer got his hot little hands on an OEM or NOS widget for your 1971 GMC truck, and decided there was a market for it, so he started the factory up making new 1971 widgets which are alllllmost as good as the original, because his tools and dies aren't quite up to snuff with GM's, or because his quality control consists of a guy named "Juan" who sleeps his shift away at the QC station. This is the bulk of parts you can find for old vehicles, and increases exponentially as the vehicle gets older and/or the part becomes ultra hard to find. It's also a minefield for people to navigate, trying to make sure you get a part that's A) right and B) will fit with a modicum of hammering and C) is the right colour, shape, and function as the part it purportedly replaces. "C" is the tricky part in most cases, because almost nobody is going to tell you "Well, this reproduction windshield wiper arm fits exactly and is just like the OEM piece for your truck except that it's purple neoprene and not chromed steel.
I got incredibly lucky once and through a quirk and a poorly written eBay auction I picked up four NOS hubcaps for my dear Rita for $30 all told, still packed in their original GM box. I had to be taken to the ER when they arrived, they were so beautiful. I've seen used OEM hubcaps go for $40 each since then, usually advertised as "Great for your daily driver!" This is secret seller's code for "I stole them off a junker in the neighbor's yard, and only had to chisel ONE of them off the rim!" And no, I won't expect to have that kind of luck EVER again. Ever.
Anyway, this all leads up to my bumper. I finally got a bumper for dear Rita (baby's got back again) and installed it last night, along with the license plate holder. And it all worked. Utterly well. Well enough that I was able to install it all alone (except for the occasional help by Mamie, the outside stray cat.) Incredible. These things don't usually happen this way, especially when the part is a toss-off of the original, and probably never even SAW an OEM bumper. But work it did, incredibly well. Mind you it still needs shimming with some washers to make it completely square to the truck, but that's a MINOR thing. The major thing is that it went on. Right. The first time. In my driveway. With ME doing it.
See, I have the mechanical skills of a King Crab. I have tools, I have the general working knowledge of how to put a nut on a bolt, but when it gets right down to it the only thing I'm good at is barking my knuckle so bad that I can see the tendons show. So naturally, it's with a bit of pride that I finished the bumper, stood up (slowly) off the driveway, touched it gently, then shook it a bit and it didn't fall off. It even looks nice. And my license plate is now out of my back window, and I'm only one horn contact away from owning an inspectable vehicle in the state of LA. It's only been just over two years now.