What is the difference between an impingement and tear of a rotator cuff?

Severity of condtion. With impingment, the rotator cuff is being pinched, without necessarily being torn, between the acromion of the shoulder blade and the top of the humerus. Raising your arm pinches the rotator cuff just like closing a door pinches your fingers if they are stuck between the door and door jam. A rotator cuff tear implies that the tendon is not simply inflamed but is partially or totally disrupted.
Injury vs tearing. Impingement implies the cuff not having enough room to move vs tearing of the cuff. Impingemnt can be caused by multiple factors and can lead to tears of the cuff.