CAD/CAM programs are used to draw the shapes of the part(s) you are making and save them in formats such as DXF. They then generate a G-Code (or tool-path) file which the machines CNC controls "understand"). The G-Code files are often named ".NC" or ".CNC". The controls load and follow/run/execute the G-Code instructions (or words as they are called) from a CNC formatted file.
During G-Code (or tool-path) generation, the CAD/CAM software passes the drawing information (vector data) through a Post Processor to generate specific information as needed for a given brand/model of control.
Different controls have slightly different requirements hence the need for different Post Processors but the generic G-Code words for motion control are the same and use Cartesian coordinates to address and specify the axes motions.
Most CNC controls do not "understand" DXF or other drawing format files directly.