Defined as measured values of reflectivity for hue, saturation and lightness.
CMYK (in ink) as in your example, defined as mixing of four theoretical inks.The measurement system allows you to peg numbers and codes to any color that is within gamut of the system. Long answer: You're dealing with two very different taxonomies of color.
This may result in small change to the color. Short answer: Map over into that new system - one appropriate for the production process - and get the customer to sign off on it.
