As one who is old enough to remember when that term was coined and used regularly (you don't hear it much anymore), that came from many swapping out their J pickups for various after market models, adding a preamp (Bartolini back in the day.. that's about all there was), and swapping out the little flimsy Fender bridge for a Badass model.
I really don't hear that term applied to Sadowsky basses, since they are really not Fendery at all.. they sound like Sadowsky's. Actually, that term really isn't used much at all any more, since it has lost most of its original meaning.
Regarding the P, there were very, very few that did similar upgrades to their P's back in the day, although some who wanted their P to sound more like a J, but didn't like the J body style or thinner neck did add a J bridge pickup. Rarely did you see a preamp added or a bridge swap (IMO and IME).
This, I believe carries over to this day, with many who want a P sort of thing going with a more traditional passive vibe, which Sadowsky really doesn't do. For example, both the Nordstrand and Alleva-Coppolo P Bass options don't have a preamp included in the spec, and the A-C P's actually coming with a very traditional style bridge as the default option.
Finally, one of the key reasons that all the boutique J's took hold (again, IME from being around when this all happened) was that Fender, for some reason, never really provided a decent 5 string J option (at least until very recently... and that is still a controversial topic... I've yet to play one that I would consider buying). So, the first big wave of guys who went the boutique route were driven there by wanting a J type instrument (P guys didn't care about this at all in general) with 5 strings, and that general trend seems to continue (regarding the sales mix of 5 strings versus 4 strings in the high end bass world, which includes the high end J based models).
If I didn't play 5 strings exclusively, I would most likely still be playing a Fender.
IMO there, but I guess about 25 years of IME with this topic.
