I think the biggest difference is just in the name.

. It just sounds less demeaning, I guess (IMO). It was over a decade ago when I was taking my 0-3 Montessori training that I first heard the term (though it was toilet learning, b.c potty wasn't the most accurate word), and it was almost like a respect thing, b/c everything else I learned about young children was about following their lead, and letting them do things at their own pace - with the adults acting as a guide.
Anyhow, to me, the process of toilet learning may consist of providing the tools - a small potty or stool to reach the real toilet, access to clean underwear, and an adult who gently reminds the child that pee and poop goes in the toilet - along with offering the opportunity to sit on it (especially after wetting), and assisting the child with changing themself. This is how we did it in the toddler classrooms I worked in, as well as how it went with my first child - who was completely out of diapers, day and night, at 24 months. It was truly effortless and gentle. Such a breeze. (now, I had 3 boys after DD and my experience and approach was not the same.

.)
Potty training, to me, brings up images of adults using coercive methods, bribes, timers, etc, maybe a struggle and frustration - even though I know not everyone goes this route and may still use the term potty training. Which is why I think the biggest thing is just the semantics of the name used.