"Does it matter who the medical services are for?"

If this is for Business, then it is Business Expense and to report it as such, you are required to use a 1099-M "Informational reporting" form.

"Dr. #2 isn't providing "medical services" to Dr. #1."

You stated Dr 1 is Paying Dr 2. That = Business expense and business relationship.

All of this part is wrong: "So is Dr. #2 just an independent contractor for Dr.#1" That just means, not acting as an Employee..." and therefore does not get a 1099" which is Wrong..."because Dr. #2 is incorporated?"

Incorporated doesn't apply to medical services. The entity Type is moot.

"So if not "medical", there would be not reason to send a 1099 to an incorporated dr.....?"

Nope. Not Medical is not that same as Incorporated or not. You are confusing too many things that are not related.

Medical services, rent to other than a Property Management Firm, and other details per box are what matters. Reportable thresholds matter, per box, aswell.

I recommend getting a copy of the Instructions for forms 1099 and also, the upcoming 1099-NEC.