I read that a G-set is a functor from a group G (considered as a one-object category) to the category Set of sets. It is a group action of G on a set (say S) in Sets. In some texts, I find that the set S is also referred to as G-set. So, how am I to comprehend a G-set? Is it the functor from G to Sets or the set S or maybe both (and we understand it through context)?