We study the relationship that exists between two families of models of product differentiation: the class of location or Hotelling-type models of horizontal differentiation, and models of vertical differentiation. Our main result is that every model belonging to a very large class of Hotelling-type models (including all the commonly used specifications) is actually a special case of a vertical product differentiation model. Formally speaking this means that the Hotelling type-model and the corresponding vertical product differentiation model are equivalent. Specifically, we show that the equilibria emerging in the two categories of models are identical in a well defined sense.