Routing is the process of hollowing out an area in a material (like composites, polymers, and soft metal) to cut various shapes in the material.
Engraving
CNC engraving is a subtractive process that removes material from a surface to create the desired shape.
Cutting
CNC cutting is achieved through friction; they use tools and bits to route into the material to get the desired through cut or a pocket.
Carving
Carving is the act of using tools to shape something from a material by scraping away portions of that material. The technique can be applied to any material that is solid enough and yet soft enough for portions to be scraped away.
