"Scrimshaw", which is performed by a "Scrimshander" is the art of carving. Carving & Scrimshaw are exactly the same thing. I think when you describe scrimshaw, you are describing engraving or etching.

Of course, I am aware of the chips you are referring to in your comparison of two methods. Lets call the one that leaves the rough edges 'engraving'. My sister used to engrave/etch such materials for a living. She tells me the rough edge cuts are probably caused by using a rotating tool such as a dremel to engrave them.