A "dent" is caused by a blunt object or by a fall to the floor. A "cut dent" is created by a narrow or sharp object made of a hard material. A "ding" is the term commonly used for a small "cut dent". It is kind of counter intuitive, but "cut dents" and "dings" are much harder to remove completely than large "dents".
The photo above shows a "cut dent" in the terminology I was taught by my mentor. See how its edges are well defined and how deep it goes into the brass. It is easy to imagine the object it came in contact with. If it were much shorter from end to end and not so deep, it would probably be called a "ding".