Wikipedia's Star domain article claims:
A similar, but distinct, concept is that of a radial set.
but the definitions seem to be equivalent. Is there some subtle difference I'm missing, or is the claim in the article wrong (or just imprecise, and referring to difference in statement of definition rather than non-equivalence)?
Let $C = \{(x,y)\in\mathbb{R}^2|xy=0\}$. Then $C$ is a star domain. But it is not a radial set. The difference is that in the definition of radial set, you look at all points in the entire space for that line segment, not just at the points in $C$.