Bell's Palsy and stroke are quite different. A Bell's Palsy occurs when there is damage to the facial nerve. The facial nerve controls the movement of most muscles of face.
There are two facial nerves, one on the right, one on the left. When damage occurs to the nerve, the entire side of the face involved becomes weak. Problems include drooling, dry eyes (from lack of control of the eyelid), and a poor aesthetic appearance. The damage is thought to occur from inflammation near the exiting point of the nerve from the skull - theoretical causes include viral infections or auto-immune diseases - both of which are very poorly understood, but usually prompt a course of treatment with anti-virals or immune suppressants.
A stroke, on the other hand, is caused by loss of blood flow to a part of the brain. When facial weakness is involved in a stroke, it almost always effects only those muscles below the eye (such as the mouth and cheeks) and not the eye or forehead. Of note, the term "mini-stroke" is one that I don't like, although some doctors use it to "sugar coat" a true stroke. A patient either has a stroke (permanent damage) or a TIA (no permanent damage). The term "mini-stroke", in my opinion, gives people a false impression that they don't have a serious disease.