The verb "умыва́ться" is used especially when the one washes his face (before or after the sleep, when the face and hands are dirty). Therefore the verb "умыва́ть" means the same but requires an object, for example:
Ма́ма умыва́ет своего́ ребёнка = A mother washes his child's face.
When you don't mean face but any other part of the body, you use the verbs "мыть","мы́ться".