CNC and DCC as I know it.

CNC as I understand it is the machine controller handles all tasks. It provides the motion commands for servos, interprets the scale feedback for closed loop systems, and also handles the programming itself (plus a myriad of others, spindle speed, coolant, etc.). Yes you can build programs on an external terminal but the program is then down loaded to the controller which executes it.

A CMM DCC machine has a controller which handles servo motion and scale feedback, (plus probing, and some others) for tach or tachless systems. The big difference is that the programming and motion commands are sent to the controller from the systems computer. You don't have a direct interface on the controller.

As far as accuracies. Some DCC controllers do not "position" as tightly as CNC Machine Tools, but some most do. Linear scale feed back, glass, metal, etc., is the most common on newer CMM's. Some older machines might have rack and pinion and rotary encoders. Some may even have rotary encoders mounted on a ball screw drive, but these are probably more common on machine tools. Machine tools "must" position very accurately, they are putting features in/on a part. A CMM can be very accurate and still not position very well. If a CMM is measuring the position of a sphere it is taking measurements off the scale as the probe takes hits on the feature. If the scales are accurate the machine reports accurate position on the sphere. In this case if you tell the machine to move to X 300mm and it stops at 299.995mm it doesn't affect accurate measurements. (most definitely some cases when this matters, surfaces, profiles, etc.)

Ball screws do "heat up" and "cool down" causing the axis to position long and short directly affecting accuracies, fans or not, controlled environment or not. Rack and pinions are ground to whatever specification the manufacturer thought adequate, and the positioning of the machine will never be better than this(a bent encoder shaft is 360 degrees of errors). These both typically have some amount of "backlash", true lost linear motion, not "fishtailing".

I don't know of any CNC controlled CMM's being sold today. I know some very good DCC CMM Controllers, and I know some not so good ones.

I'm no engineer, but this is how I understand CNC and DCC Controllers.