Cold Extrusion and Cold Drawn......
In extrusion processes you are pushing the metal through a die, while in the drawing process you are pulling it. Usually. That said, it really doesn’t make a difference, as you can get similar properties through either process. The important factors are how much reduction in area you are achieving, what the condition of the starting material was, and whether you are giving the metal an anneal during the process.
There are times that the cold deformation process must be designed to give properties that fit certain specifications. Alloy C17200 beryllium copper 1 inch diameter rounds, for example, must demonstrate a tensile strength of 90 to 125 ksi to meet ASTM B196. That cold working can be done by extrusion, drawing, rolling, forging, coining, hammering, or telekinesis; it doesn’t matter.
It isn’t obvious, but the condition of your purchased metal usually defines the tolerance table. So while I may not care about the additional strength I might get in going from hot-rolled to cold-rolled, I certainly do care about the straightness, bow, camber, and dimensional variation acceptability.