Since I play bass I will tackle this question from a bass guitar perspective.
I've had some musicians state that the following tuning is Drop C tuning (E is dropped to D, and then all strings are dropped 1 additional step):
C - G - C - F
I've also had other musicians that state the following tuning is Drop C (only E string is dropped to C):
C - A - D - G
I always assumed Drop C was the later version (only E string), since Drop D tuning is when only the E string is dropped. However, many bass/guitar players I talk to disagree with this. What is the correct definition of Drop C tuning?