Have to confess I never followed them, or the whole "grunge scene" if that's an appropriate classification. But the samples you've posted reveal a terrific talent, and one that left us too soon.
To clarify, You are correct in the statement of Classification, in that STP just got "Chucked in " with the grunge bands. It has been documented in a few different articles I have read that the real "Grunge" bands did not care for them that much. STP was really just a hard ricking band. They embraced "Arena rock" and were very near flirting with heavy metal.
BGD gave some great examples but I have to say that THIS is my desert island STP song. DEAD AND BLOATED ( add headphones and crank it up!) https://www.youtube.com/watch?v=MdCEPhNBnrM