This paper confronts renormalization used in quantum field theory and that used in critical phenomena studies in statistical mechanics or dynamical systems theory. Regularization that cures spurious divergences is distinguished from renormalization transformations allowing to compute actual physical divergences. The former generates a group, and is also encountered in singular perturbation analyses in nonlinear physics. The latter generates a semi-group, and is implemented as a flow in a space of models; its analysis, focusing on fixed points and their neighborhood, allows one to determine asymptotic scaling behavior, to delineate universality classes and to assess model structural stability (or instability, i.e. crossovers). The renormalization group can be seen as a symmetry group and a general covariant formulation is proposed. Aspects presented here show that renormalization theory has emulated a shift of focus from the investigation of outcomes of a given model to the analysis of models themselves, by relating models of the same system at different scales or grouping models of different systems exhibiting the same large-scale behavior. So doing,not only (subjective and partial) models are distinguished from underlying physical systems, but also intrinsic physical features can be derived from model comparison and classification.