That's the common usage, but they are more general than that. The degree of continuity can vary from knot point to knot point depending on the multiplicity of the knot point. I'm not up on current reference material, de Boor isn't the easiest read, and wikipedia hasn't the depth. Hmm. There is some course material online that is sometimes good. In any case, it takes some study to get past the easy part and the only general definitions I'm aware of are rather abstract. Things might have improved since I was reading in the subject.