Swinging is its own thing--it's for romantically monogamous couples to have recreational sex and partner-swapping without falling in love with the other people.
That's not the only way to have group sex, of course. It's kind of annoying to me when people say that any sort of group sex thing is "swinging."
For my partner, although he doesn't get invited to as many sex parties as he would like LOL, the communities having these parties involve either queer people, kinky people, people who go to Burning Man, etc. None of them would call themselves swingers.
What's interesting to me is that these people ALL seem to be polyamorous. Not that everyone at these sex parties is in love with each other, but that almost everyone there identifies as polyamorous and has multiple relationships (with people who may or may not be at the sex party). This phenomenon may be local to the area--I'm talking about people mostly around Somerville, Massachusetts (of course, LOL).
I know quite a few triads of various gender configurations--more than I would have guessed is the "norm" from reading this forum. None of them use the word "throuple" though! And also, none of them are the unicorn hunter MF+F triad we see so often here.
I do understand your frustration, Mags, about pop culture equating group sex with polyamory. I, personally, would pay good money to NEVER attend a sex party (or Burning Man, for that matter!) but I will always be polyamorous.
But, my point is, quite a lot of polyamorous people, in my experience, do also enjoy group sex stuff. Or, to think of it another way, people who like group sex often find that polyamory is the best relationship model for them.
I don't think the difference is as stark as you make it out to be. There is a lot more overlap than "group sex is NOT poly!" would imply.
I would definitely like to see SEPARATE poly relationships portrayed in pop culture. But a show that briefly portrays a MFM triad as kind of normal sounds like a good start, actually.