How is the idea of morphisms between objects in category theory different from the idea of relations between sets in set theory?

Question

If possible, please also give examples where the latter is not the former and vice-versa:)

I'm having much trouble distinguishing these ideas. In set theory, you can have multiple sets $A$, $B$ and $C$....which are collections of elements, and you can have relations among them $R_{AB}, R_{BC}, R_{AC}.... $

Let's name the set of above sets a "category set". Now one may take multiple category sets and define relations among them. Let's name the set of these sets a "Functor".

I want to know, how are these ideas different from the corresponding ideas in category theory?

Answer 1

Only certain relations will give a category. At a minimum to be a category you need identity morhisms and to make sure composition of morphisms are defined. This means that only relations that are reflexive and transitive will form a category.