From listening to a few seconds of those videos above by Azmodeus, I take it alternative music is something totally different from Alternative Rock.

To me, Alternative Rock began in the early 80's as a non-commercialized real/raw music to be contrary to the popular radio stations which were being quickly taken over by R&B music. Alternative music allowed for a non-standard rock choice that included influences from the best of the 60's and 70's rock, folk, and punk bands that those at the time had grown up listening in their youth.
As groups like the Police, Queen, the Who, Rolling Stones, and Led Zeppelin were retiring or not producing like they had in the past, there was a need for the alternative. In came groups like R.E.M., U2, Red Hot Chili Peppers, Smashing Pumpkins, Pearl Jam and Nirvana to fill a void, a void that seemed to be completed when the Police broke up. The Police were pretty much the most popular rock group when they suddenly broke up during their Synchronicity tour.