Refutation: A counterexample to the premise of the argument and a contradiction

peace!
Refuting a claim or statement is possible in two ways: Providing a counterexample. on. Making the argument and arriving at a contradiction.
Is there a difference or preference for the second over the first? It feels as if the second ‘explains’ the fallacy of the claim better, but is there really a logical definition for ‘explained proof’ that something is wrong, as opposed to a ‘counterexample’? On the face of it, both are logically valid, so which is ‘more valid’?
I hope I understood.