At the same time, they dropped the original "Apple Watch (1st generation)" and replaced it with "Series 1", which as far as most users were concerned is basically the same thing, but it has a slightly faster processor than the original.
I wouldn't be surprised to see "Series 0" get dropped sooner rather than later. The iPad analogy is a good fit, the very first one is stuck at iOS 5, but anything newer than that gets iOS 9 at a minimum.
Re: terminology, "Series 0" is definitely not an official name for it, just a convenient shorthand that feels easier to understand than its official name to me.
So we end up with a classic fence-post error, where if I say I have the first model, most people could assume I mean Series 1. So we've taken to calling it Series 0 (a term Apple never used/uses). Otherwise if I just call it "Apple Watch", you have no idea if I'm implying a version number or not.
I get their problem. "Series 1" is less "2nd generation" and more "revision 1.1". If they'd called it a 2nd generation, they'd overpromise and under-deliver, which is never popular. But calling the 2nd revision "Series 1" is all kinds of confusion.
Series 1 was the orignal Apple Watch with a better processor and a price cut. Series 2 debuted a the same time and added more features like water resistance and a brighter screen.
Which, if you google it, is actually a model name. You can find repair guides, guides on upgrading, teardowns, etc using that phrase.