For example if the tuning is
C A D G B E
What is that called? Not Drop C is it?
Some people understand "drop C" to mean CGCFAD (or, drop D transposed down a whole step). Other people understand "drop C" to mean CADGBE (or, standard tuning, and you drop your E to C). So I would not just call it "drop C".
A somewhat common and less ambiguous name would be "E drop C" - since you are tuning to E and then dropping the E to C. Then the other "drop C" would be called "D drop C", by the same logic.
In writing, I would just write "CADGBE" tuning. It's clearer, more widely understood, and no longer to write out than "E drop C". At the very least, if you want to call it something else, you should start by saying the term you chose to use means "CADGBE" tuning.
So there are two ideas going here and both are correct.
The "drop" on Drop D, I believe, refers only to dropping the string down to D. However, the reason that works so well and is so widely used is because then the lowest three strings form a power chord DAD, which makes playing power chords easier in rock music because you can just lay one finger down and cover all three.
While this tuning could be called Drop C (what determines that is how often that term gets used by musicians and then it just becomes known, it isn't simply a matter of defining it in text book/dictionary sense), it also does not serve a similar useful function on the guitar as Drop D. But ya, you could call this drop C, however if no one knows what you mean by that, what difference does it make?
I think the above discussions show that simply applying a label to it is kind of a moot point unless everyone is on the same page, and since this tuning isn't a very widely used one, you will have conflicting ideas.