Some of my professors it is awkward when see them off campus and others it is not, just like any relationship as some people you hit it off with and others you don't. When I used to teach in the corporate field, the same thing would happen; some would be uncomfortable talking if ran into to them outside of class and others not. Always tried to keep conversations brief though.

What is more awkward to me is that transition from last name to first name. This is more uncomfortable to me even being an older student. Especially if it is during a semester, when other classmates are still calling them by their last name and I have been asked to call them by their first. I can't do it in front of others, still insist on using their last name.