This is a very interesting question. There are several differences that come to mind. First, when you look at yourself in the mirror, you are the one doing it. There is an element of self-will. However, when you look at a photograph of your face, it is someone else's view of who you are. So, there is a lack self-will.
Second, there is the importance of perspective. When you look at yourself in the mirror, you can change the perspective of your view. For instance, you can look at yourself from different angles. You can also zoom in or zoom out by stepping closer or further away from the mirror. The possibilities are endless. When someone takes a picture of you, it is their perspective. You have little choice. It is the way that they see you that has the focus.
In the end, the difference is in the eye of the beholder. With a mirror, you are the beholder; in the photo, someone else is the beholder and you are looking at their work.