You are pretty close. The American Medical Association, (AMA), and the American Dental Association, (ADA), are the 2 different medical organizations that represent each group. Originally, they tried to set up one association but the dentists decided to form their own group. This has lead to group bargaining with insurance companies. Which leads to separate policies being needed.
I used to get really bad ingrown toenails, I had a podiatrist cut about 1/4 of that toenail out so it can't grow back in that spot. I don't remember it being very expensive at all. But this was 10 years ago