Research MD vs. practicing physician
Male vs. Female
Beginning of life (OB) vs. geriatrics/hospice
MD vs. DC or DDS
One end of the body vs. the other end (I won't spell that out )
I thought there might be a Nat/Kat connection, but nothing so far.
While any of this could be true, just wanted to mention again that someone with a PhD (e.g., a professor) would also be referred to as "Dr." and it wouldn't have to have anything to do with medicine - could be a historian, for example. A PhD. is what comes to mind for me when I hear the phrase, "the other kind of doctor". It could also be a non-MD person in the medical field, someone in biology, chemistry, etc.
Remember in Season 17 where Chad taunts Nat "How's that PhD working for you?" and she responds, "For the record, I have an MD."
There's a lot of colleges in the LA area. Maybe they are friends of Nat and Kat, whether or not medical people - I think Nat and Kat went to UCLA, no?
By "opposite" kind of doctors, could they be talking about psychiatry or psychology? As in mind vs. body.
That's possible too - a psychologist would have a PhD while a psychiatrist would be an MD.
Also, Winnie could be short for Winifred, though I expect people have thought of that.