I have kind of adapted myself to using the term epicycloid to collectively describe what most folks call Spirographs.
Truthfully, there are several kinds of mathematical curves that can be used to even more carefully note which is which amidst these special kinds of curves. I am not a mathematician by any stretch of the imagination; my innumeracy gives me problems with even simple math. (Doesn't mean I find it any less interesting!) For those who wish, a good general description of epicycloids and their kin can be found here.