Leaving aside the "tarred with this brush" aspect of the OP and looking at the question: can they be more positively distinguished?
Yes they can, by renaming them. Should they be? No.
I will hold my hands up and say that when the doctor said to me "you have type 1 diabetes", my response was to stare vacantly at him wondering "what the Hell is that then?". So, sorry Martin Luther King but I was sincerely ignorant. That said, I had no involvement with diabetes through family, friends, education or work.
Point is, everyone can't know everything about all the conditions and ailments out there. The secondary, and perhaps bigger point, is that when people are ignorant they will do one of two things: 1. Ask questions and seek to learn. 2. Say the first thing that comes to mind.
Approximately 6hrs after the Doc told me that I was leaving the hospital having been educated on diabetes. Do I worry or care of people can't tell the difference? No way. I have enough to concern myself with in life without that!!