According to MushroomExpert.com:

“Three species, Craterellus cornucopioides, Craterellus fallax, and Craterellus konradii, have been separated on the basis of geographical distribution and the color of the spore-bearing surface. Dahlman et al. synonymize all of these species, finding no significant genetic variance. The name Craterellus cornucopioides takes precedence according to the rules governing botanical names.”

C. konradii was also separated based on color (yellow/orange vs. black), but many examples have since been found of the the two color forms growing in the same cluster. See observation 2828 for an example of the yellow/orange form.