CD: the kind you buy from a store with content already on it. Mass-produced with methods and equipment not available in the consumer electronics market, because it was never really necessary. Also includes CD-ROM (Read Only Memory) for data/files read by a computer instead of music alone
CD-R (Recordable): can be written ("burned") once and only once. As mentioned in another comment, it may deteriorate over time because of how the disc gets written, but by the time that happens you'll probably forget you had that disc
CD-RW (ReWriteable): Can be written like a CD-R, but you can also erase it and write on it again. More expensive, and I believe some readers had trouble with it, but in a world where data storage was expensive and small this was still a useful thing to have
DVDs had a similar thing, except there were variants where the - was a +, eg DVD+R and DVD+RW. I can't remember the difference there, but it was pretty trivial. There was also a relatively obscure DVD-RAM that had random access memory. That was pretty cool as well, kind of an alternative to DVR that wasn't a VHS tape. No need to lose everything you had if you wanted to add more to it
The difference between DVD-R and DVD+R is how tracking/timing metadata is encoded on the disc. As manufactured, the disc isn't entirely "blank," it's got tracks for the laser to follow already on it, which include timing marks to help the drive track and index the data. -R and +R discs use different techniques for doing this, almost entirely because Sony just can't handle anything that isn't their own in-house proprietary shit.
This didn't effect playback. Once the disc was burned, that metadata was still there but an ordinary DVD-ROM drive (or DVD movie player) wouldn't even look for it, for playback, it looks like any other disc. It was only an issue for recording, and as a user you had to know which your DVD burner was capable of using so you could buy the correct discs. Eventually DVD burners were built to handle both, and today unless you have some vintage equipment it's a non-issue.
I'm a mid-to-older millennial. My elders would say shit like "What? You don't know how to use a gramophone? You young whippersnappers are completely worthless." And I find that behavior absolutely abhorrent.
If you were here in person, I'd offer to spend some time burning some CDs. I've still got a computer with some pretty decent optical drives laying around. I can probably even scare up some blank discs. We'd find some music, burn it to a disc and then try it out on my old boom box.
And weird bugs like Windows audio somehow creeping into audio CD burns. Or the times in Linux where the tray would refuse to open or close. I used to keep a paper clip next to my next to force it open sometimes....
I had pretty good luck burning discs, they would occasionally fail.
I had a CD-RW I used for my mp3 player, and the software I used (Roxio) had this mode where you could treat the disc like any other mass storage device, you could add a single file.
For our young friend SagXD, burning a CD usually had to be done as a whole. You'd arrange all the files (if a data disc) or audio tracks (if an audio disc) in a buffer, and then burn the entire disc in one shot. If done at "1x" speed, it could take an hour, but "8x" speeds were pretty common, if more error prone. With my rewritable CD, I could add a single file if I wanted to and not have to rewrite the entire disc. Adding a single song to the iPod I got in college wasn't much less rigamarole.
If you're an asshole to a kid ironically, and the kid thinks you're an asshole, you're just an asshole. An entire generation wasn't taught that, and look at the world they built.
Don't hate it! You were just born in a different time. Your time will come where you have to explain to the young ones about how "smart phones" worked since they'll just have their implants as interfaces. And also jetpacks.