In the last decades, the linear parameter varying (LPV) and Takagi-Sugeno (TS) fuzzy paradigms have been applied successfully to nonlinear systems. Despite the strong similarities between the two paradigms, they are considered different by the academic community. This paper discusses the analogies between the two paradigms when applied to the control of non-linear systems. After establishing a link between the modelling framework, the conditions under which the obtained controllers lead to equivalent control laws are presented. The discussion is completed by an application example which serves to illustrate the analogies and equivalences presented in the paper.