You're correct, there are some more sophisticated processes used by specialty printers such as CcMmYK (https://en.wikipedia.org/wiki/CcMmYK_color_model). Something like this will use more inks and less halftones, giving better results in some cases.

Or are you referring to other printing methods, say for example silk screening? There, you would definitely select a specific ink to use. It just depends on what your goals are.

Or they could be referring to Spot Color.