I think there is a more noticeable split between fellowship trained v not, especially the "dabble on weekends" type or generalists who take a weekend course and think they can just become a specialist (whether that be neuro, rehab, health, etc).
For some people, there is a split between neuro v rehab+neuro fellowships. I haven't stayed up with the particulars over the past decade or so, but there has also been a shift in the field that made the nit-picking a bit less applicable. Neuro and Rehab have crossover, and it irked some in neuro bak when I trained that rehab also did neuropsych testing, though at some point, neuro started crossing more over the rehab and that ruffled feathers too; this is where day-to-day practice blurs a bit.
Someone more in the know can speak to this better, as there have been multiple gatherings by Div 40 and Div 22 over the past decade meant to address some of this. Once I left my last AMC, I stopped tracking and caring as much about this kind of stuff.
The bottom line is competency and scope of practice. Much like a psychiatrist does perform general surgery, even if their licensure allows it. Clinicians should only work in areas they have adequate training. Practically, splitting hairs is mostly ego, but some people still care.
Edited to simplify, as there is a lot of behind the scenes stuff aka “politics”, so I cut that stuff out.