Name two "different professions entirely" that have the same governing body. I can't think of one instance where that's true. Here in the U.S., it's not like the Federal Communications Commission oversees the Federal Reserve.
And because you cant think of any, it means that none exist? I'd love to have you as a med student.

Paramedics and chemical shipping companies are both governed by the DOT/NHTSA
In my state, Acupuncturists, Electrolysis techs, and .... wait for it...... wait for it..... Midwives... are under the same governing body.
The USDA has committees on Nutrition as well as Forest fire prevention.
.... whatever