For color perception there is no difference. Observer sense a color without any data of the stimulus origin.
The term Digital colors could be associated to the way how one control light source or how analyze color. In the case that color red green and blue components are controlled in the certain number of digital levels (e.g. 256 each), one can to say that color is digitally controlled or color content is digitally expressed. To provide capability to calculate color coordinates for such source one need to know color channel spectral properties and intensity level.
Chromatic Color could be associate to specific color coordinate value on the CIE Chromatic chart.
May be this answer is not complete, but you need to learn more about color perception and colorimetry. There are a lot of nicely written books on that topic. Color science is exciting topic and you should enjoy learning more.
Chromatic colors have spectral characterizing hues: red, blue and yellow (and a variety of the mixes in between, of course). In this question, I think, chromatic colors should rather be compared with achromatic ones: a mix of white, greyish hews and black. I think, both categories can be digital as soon as they are represented by the computer bit systems.