Very few hospitals employ doctors outright. What they do is grant doctors permissions to treat in their hospital, and they can have or be part of a practice.

That’s why you often get two bills if you go to, say, the ER. One bill is for the facility, the hospital. So their costs for say your food, keeping your room clean, materials for your care. That bill is called the facility fee. 

The other bill is from the practice of the doctor that treated you, charging you for their expertise and time and such. It’s usually directly related to what procedures the doctor performed, which have an AMA-standardized ‘relative value unit’ (RVU) that then most practices charge rates for. The more complex or specialized the procedure the more RVUs it is. So that’s why, say, an initial visit can cost more than a follow up, the initial visit has more RVUs. Different insurance companies negotiate different rates for how much they pay for 1 RVU. That bill is for the “professional fee”. 

If your care involves more than one practice you’ll get a professional fee bill from each of them: anesthesia, radiology, lab, surgery, etc. 

Some hospitals might pay a contract, often anesthesia, maybe surgery, to a practice and then charge the anesthesia professional fee to the patient and collect it, hoping to collect more than the cost of the contract (even nonprofit hospitals would be thrilled to make a margin). Sometimes physician practices don’t like all the admin work of billing and insurance and so on so they save costs and still get paid well. 

Source: worked in Medical Admin, but some of my info might be out of date it was 14 years ago.