I break that down this way:
Nirvana was alternative.
Grunge was not alternative. Grunge was a mainstream rock sub-genre created to capitalize on the popularity of Nirvana. Grunge caused hair-metal bands to ditch their hairspray and shop at K-mart for flannel shirts.
Alternative, as defined in the nineties, was not alternative. It was the dominant rock genre, fully supported by the major labels.
Nu-metal succeeded Grunge as the primary thrust of rock, trading as "Alternative".
Meanwhile, some non-Alternative alternative artists kept doing things that were different. Sonic Youth, Bjork, Beck, Morphine...
Completely agree with this. I absolutely hate that grunge ever was associated with alternative. Nirvana was one thing. But the whole grunge movement in general was just a spin off of metalish rock and had way more in common with what I would say became Active Rock. I fell into the grunge trap myself, but looking back I can't stand 90% of it any more. It IS active rock. Maybe it gave alternative stations a boost but, with the exception of most of Nirvana's material (which even now I am tired of), there's little of what made alternative a format for truly great bands from the Pixies and Echo & the Bunnymen to punk bands like the Ramones.
I think the grunge era was the worst period for Alternative. Go back to the playlists of WHFS. That's alternative.