A grimace is the look on your face when you experience pain, smell or taste something bad. If you suck on a sour lemon, your will probably grimace because of the sour taste.
When you mug, you make a special face, pleasant or unpleasant, posing for a camera to attract attention to the photo. If you are mugging for the camera, you are usually having some fun. If you are grimacing, you are experiencing something unpleasant or trying to look unpleasant.