I think it's pretty rare for someone to mention degree in a conversation, especially if they you preface with the words, "physician" or "medical student." However, if someone does bring degree into the conversation, this probably implies that they know there is more than one degree for physicians. In that case, I would guess they know or at least have heard of DO's. So if someone asks, "Oh, you're an MD?" I might respond with, "No, I'm actually a DO." The only way to answer that direct question is to be completely factual.
Your response, while it avoids bringing up osteopathic medicine, might not be legally correct. Technically, the MD degree goes with "Medical Doctor" and the DO degree goes with "Doctor of Osteopathic Medicine." It might slide in casual conversation, but probably wouldn't work in a court of law.
What's true for me right now is that, "I'm a 2nd year medical student." That's generally how I respond. Usually, people then ask where I go to school, I respond, "Kansas City, MO." Sometimes, people will ask what school I attend, in which case, I simply tell them, "KCUMB, previously known as UHS." Locally, many people actually recognize the name and know what I'm talking about. However, if I'm out of state, people usually just go, "Oh" and the conversation generally shifts elsewhere, usually to, "what specialty are you interested in practicing when you finish school?" If they say they never heard of the school, I tell them there are three medical schools in the Kansas City area and name them. If I feel it'll be meaningful to the conversation, I might say specifically that my school is an osteopathic medical school. In any case, I've never had anyone question that I am going to be a physician or anything like that. Never had any issue with anything related to cocktail conversation on this matter...then again, I tend not to like small talk and avoid meaningless banter in general.
