Exactly, its all rock and roll, just one of the many flavors, and more often the labels are associated with the region the current trendy music is coming from. You had "Southern Rock" in the 70's, the "NWOBHM"(New Wave of British Heavy Metal) out of UK in the late 70s early 80s, then it was "hair metal" in LA through the 80s, and of course when Seattle bands took off in the 90s someone coined "grunge".
Soundgarden were most definitely grunge, and I believe the term applied to the Seattle sound at the time because the bands were dressed "grungy", i.e tore up jeans, flannels, combat boots. Which was quite the opposite coming on the heels of the 80s hair metal/glam scene.
I'd probably go to this if I was in the area. I first got turned onto Soundgarden sometime in 1987 or '88 visiting a friend who was attending SUNY New Paltz. I'm pretty sure they didn't call it grunge at that time, was just a new band to check out. He played me their Screaming Life/Fopp EP stuff from Sub Pop records. It blew me away, the way they played and the sounds they were creating. I felt the band name was appropriate, especially with headphones it was like being in a garden of sound. These screeching, plodding riffs and doomsday sounding guitars and yet really no flashy guitar god type solos. The vocals were insane, the way the guy could belt it out instantly impressed me. All those things hit me at once listening to this new breed of hard rock I thought oh man, this is awesome, and I've been hooked since. Its no wonder they hit it big time.
IMO I think the industry needs a new wave of rock and roll from somewhere, all this Taylor Swift, and auto-tune rap tunes are hard to listen to when you grew up listening to guitar oriented rock. I might be out of touch, I dunno, but all the rock radio stations I tune into play old classics, where is the next wave of new rock happening? Is there one?