Some people there's almost no difference and on others there is a huge difference. Try they both on and take a look. Cs are usually more yellow or olive then a normal NC.
If you're not sure which will suit you best go into the store or a counter and try on an NC, C, N, and an NW so you can see all the differences. I usually have no problem doing that for customers. I perfer to do that and help you find the color you're happy with then have you bring it back cause you're not sure.I have customers who would look better (in my opinion) with an NC but they personally perfer and NW.