AbstractVan Trijp (2013,2014) claims that Sign-Based Construction Grammar (SBCG) and Head-Driven Phrase Structure Grammar (HPSG) are fundamentally different from Fluid Construction Grammar (FCG). He claims that the former approaches are generative ones while the latter is a cognitive-functional one. I argue that it is not legitimate to draw these distinctions on the basis of what is done in FCG. Van Trijp claims that there are differences in the scientific model, the linguistic approach, formalization, the way constructions are seen, and in terms of processing. This paper discusses all these alleged differences. Van Trijp also claims that his cognitive-functional approach is superior in terms of completeness, explanatory adequacy, and theoretical parsimony. In order to facilitate a discussion and comparison, I introduce the reader to basic assumptions made in FCG and the analyses suggested by Van Trijp: I first deal with the representations that are used in FCG, talk about argument structure constructions, the combination operations fusion and merging that are used in FCG, I than discuss the analysis of nonlocal dependencies and show that the suggested FCG analysis is not explanatorily adequate since it is not descriptively adequate and that a full formalization of approaches with discontinuous constituents is not more parsimonious than existing HPSG analyses either. After the discussion of specific analyses, I then provide a detailed comparison of FCG and SBCG/HPSG and discuss questions like the competence/performance distinction, mathematical formalization vs. computer implementation, fuzziness and fluidity in grammars, and permissiveness of theories. I conclude that HPSG, SBCG, and FCG belong to the same family of theories and that all claims to the contrary are unjustified.