Pshh... Unfortunately things aren't that consistent or that would have been pointed out much earlier. C to C# and C to D are both considered 'steps' (see 'stepwise motion'). That is to say, "half" and "whole" are treated like two different types of steps in traditional theory. (that and "whole" is a much less useful fundamental unit as I said before)
What? I'm lost. How can a step possibly mean a half step? A step is a whole step. Anything else is madness.