My research in NC has shown that the Free Negro designation was used to indicate that the person had not been born free or were freed slaves vice free people of color who were born free while mullato was usually based on skin color. The person taking the census could not discern what the racial makeup was.
Also if you look at the NC census for the most part you will not see an Indian designation especially in the earlier censuses. This was supposedly an attempt to eradicate Indians and they were listed as free persons of color with the race being designated as mullatto, white, or sometimes black depending on their spouse and children.