I'm not sure what you have read about unschooling to give you that impression but from my reading unschooling is very well defined no matter who is speaking or writing about it (there is actually an unschooling conference on in Australia at the moment which is pretty exciting - ALLive). At its core, it is a form of home education, if you are not home educating than you can't be unschooling. It would be like somebody who isn't a parent saying they gentle parent - some of the principles may guide some of their decisions but without the parenting part then it isn't the same thing.

You can call what you do unschooling, you don't need my approval to use the word obviously, I just disagree that it applies. And I think there would be more helpful descriptions; possibly something like "children as people parenting" or "respect based parenting" or "partnership parenting" - if you just want to say you follow their curiosities outside of school and think that is an important part of education then I do think that is just being an active and involved parent and that is the really shallow depths of unschooling, it is much more than that (yes it is a spectrum but one that begins at rejecting school).

I won't keep rehashing though, my position on the matter has been communicated and what you take from that is up to you, I hope it is something helpful even if you still disagree