Paper aims to unify in a one-and-only theory several generalizations of the notion of metric as well as its probabilistic versions. We establish that the following well-known metrics are very special cases namely, Ultrametric, b-Metric, Probabilistic b-Metric, Branciari Metric and Probabilistic Generalized Metric. Our approach pushed us to generalize and study the Banach contraction principle in the framework of this unification.