We will explore two natural definitions for Sobolev spaces within the context of mappings into a Banach space: the classical definition via distributional derivatives and the so called Sobolev- Reshetnyak space of mapping whose scalarization via functionals lies in the Sobolev space with uniform control on the gradients. We will discuss the differences between these two spaces and how their equality characterizes the Radon-Nikodým Property for the target Banach space, and we will also give characterizations of the Sobolev-Reshetnyak space using metric and w*-derivatives.