I've never heard of Trekkies as a generational term. I've always understood that Trekkers were people who enjoyed the show as a show (they're on the Trek) whereas Trekkies enjoy the show as part of the show (they're in the Trek). Like they believe Trek is real, or it's our actual future, and that Klingons and Vulcans are out there somewhere. Gene Roddenberry preferred this term because the show is about hope, that things will get better to where the show is, and that when things are bad on the show, hope that they will be better or that it will all work out in the end. But me? I just like it as a show. It's not "real" to me.

Though, I suppose everyone's relationship with Star Trek (or, any other franchise) is unique and personal to them and you can't just divide the fans into two categories. Still, that is what I always understood the difference between the two types was, as we are a franchise that has two names for its fans.

Regarding what you said about them having a generic space show and naming it Star Trek. That has happened before. Deep Space Nine exists because the guy made Babylon 5 pitched it to Paramount and they ran him off and stole his idea. Yes, Deep Space Nine is awesome and we love it, but it would not exist if not for Babylon 5, which we should all be thankful we also got. To this day no one who wasn't involved knows exactly how much DS9 took from B5, but DS9 was not originally Star Trek, and it was widely criticised for not being Star Trek being that they were not exploring and that they were on a space station. I imagine a lot of episodes of TV started out as something else, some unconnected idea that was shoehorned into that show in the writers room. So while I don't doubt that Discovery may have not been an original Trek idea, I do not care because neither was DS9 and I love DS9.

I'm not disagreeing with you, though, and I agree with some of your clarifications, particularly in point 1.