Apparent Conflict.
You know what phrase bugs me? "The appearance of a conflict of interest." Discussions of ethics rules invariably get around to someone saying, "we want to avoid even the appearance of a conflict of interest." Or using phrases like "rules or practices designed to prevent conflicts of interest and the appearance of conflicts of interest." But in reality, you either have a conflict of interest in a particular set of circumstances or you don't. Calling it only an "appearance" of a conflict is just a lame way of saying, "some people might have a problem under these circumstances, but a principled person like me could never be conflicted about the right thing to do." Appearing to have a conflict of interest and actually having one are exactly the same thing. And when you have one, either you are tempted to act inappropriately as a result of the conflict or you aren't.
Update: Here's an attempt by the Seattle city government to explain the distinction. I'm still not persuaded. Both of their examples look to me like situations where somebody has a conflict of interest. The second one is just a little more benign.