An animal can be born deaf (congenital deafness) or it could acquire the deafness during the course of its life. For an animal to be considered totally deaf, the problem must greatly affect hearing in both ears.
Congenital deafness
(= inherited deafness)
Certain breeds predispose to deafness. The incidence of deafness among Dalmatians (and any dog with predominant white coats, it seems) is relatively high. Dalmatians (you remember them from the Walt Disney movie) are a weird breed anyway. For example,