Let's call one doctor Ted and the other doctor Bob. We will also replace the verb "to doctor" with "to treat". We will say that Bob is sick and Ted is doing the treatment. So, "the doctor doing the doctoring" is Ted.
Now it will be easy to understand:
When Ted treats Bob, does Ted do the treatment in the the way that Bob would as a doctor, or does Ted do the treatment the way he (Ted) usually treats someone?
That is, will Ted say, "Bob, you are a doctor. How would you like me to treat you for this?" Or will Ted just think, "I am a doctor, too. I will treat Bob how I feel is best"?