The type of material and eventual surface coating for the cutting tool determine greatly effects its ability to cut in different materials.
Cutting tools used for operations where a cutting edge removes material from a workpiece, usually called Machining, can be grouped according to the material used for the actual cutting edge:
Cutting tools of Cemented Carbide
Cutting tool made of cemented carbide powder that is pressed or metal injection molded (MIM) followed by sintering
Cutting tools of Polycrystalline diamond
Cutting tool where the cutting edge material holds grains of natural or synthetic diamond