The thing is unsigned soloists, duos and small groups playing non mainstream music (at the time) goes way back. And of course they didn’t start out being signed to some label. So perhaps it’s just a newer term for the same old thing?
That's one way of looking at it.
At one time, the only way to put out a record was either as a vanity record or on a "label." This meant that, although there were still plenty of "unsigned artists" playing clubs and shows, there were far fewer records made. Now that anyone can make and distribute a "record" from his spare bedroom or garage, there are millions of these recordings thrust on the public. Now, it's not just a music hobbyist or aspiring recording star, it's a "thing." These days, there has to be a name for every "thing," so the keeper of all names gave us "independent artist," which sounds pretty respectable - better than "vanity pressing" or "unsigned."