Back to the sixties....
Women cooked.
Men worked for $50 a week.
Life was simpler, then...
Everyone smoked cigarettes.
TV was not yet affordable.
Musicians could barely afford musical instruments. They had pawnshops for that.
Sixty watt (peak) amps were standard and you got it from a Radio Repair Shop.
The upright doghouse ruled the stage.
Rock did not exist. Leo Fender made basses for C&W, R&B and R&R.
People who bought an electric bass guitar were into the music of the time. That's why the Telecaster Bass and the Precision Bass are the way they are. But there grew a number of folks who wanted a jazzier sounding bass, similar in tone to the upright and with a fast action neck.
So, Leo designed the Jazz Bass. You had to make a choice... J or P, what's it gonna be?
With the advent of affluence, ordinary musicians could order customized basses or commit DIY mods. It started with Badass Bridges. Then Jaco got everyone to dump the ashtray covers.
Then PUP swaps became the rage. Boutique suppliers popped up. Now in the age of Frankenstein, one can own a P/J or a J/P. And all manufacturers have followed suit; every one of them plagiarizing Leo Fender's toy bass.
The tampering started with Dick Dale and ended with Jaco Pastorius. Now, a fellow living in his mother's basement can dream up any combination and add the expense to his mother's mortgage. The notion of mis-naming referred to in this post is due to a lack of knowledge of history and common sense. Just as fifty's kids hot-rodded the ol' jalopies, kids today drive the post-retail market for the same reasons... identity, novelty and "look at me - I'm different!" Nothing wrong with that, eh...? We all want to look different!