For example, the level curve of a function that takes two variables ($x$ and $y$ for example) and a parametric equation involving two functions ($x=f(t)=...$ and $y=g(t)=...$). Both of the resulting graphs would be in two dimensional space I believe.
Both of these ideas involving forming a graph determined by a single variable.
I think there is some fundamental difference that I seem to be missing. I've been thinking about this for a long time but maybe my line of thought is in the wrong direction, any help is appreciated.