I've typically responded by indicating that CHC theory is the broad umbrella term for the most empirically supported psychometric structural theory of intelligence, and Cattell-Horn and Carroll simply have two different "flavors" of frameworks (models) for organizing and explaining the underlying structural elements. Stated more simply....CHC theory is the broad umbrella term that subsumes these two promient models.
I just ran across a quote that, I believe, supports my arm-chair distinction between the related concepts of a theory and a model. Below is a small section from the introduction of the following article. I think it supports the idea of a broad CHC theory under which there are two prominent specifications/organizations of the primary elements of the theory....aka, the Cattell-Horn and the Carroll models. I hope this helps.
Karr, C. A., & Larson, L. M. (2005). Use of theory-driven research in counseling: Investigating three counseling psychology journals from 1990 to 1999. Counseling Psychologist, 33(3), 299-326.
- "The definition of theory used for this study was “a general principle formulated to explain a group of related phenomena” (Chaplin, 1985, p. 467). For the purposes of this study, a model was construed as “a description of the assumed structure of a set of observations” (Everitt &Wykes, 1999, p. 119). Although similar, the former utilizes a general tenet to explain related interactions, while the latter describes the expected observable interactions in more detail. By definition, theories and models are similar in function and scope. Forster (2000) stated that the best way to distinguish theories and models is to discuss each in conjunction with predictive hypotheses. In his conceptualization, the three are hierarchically arranged, with “theories at the most general level, models applied to concrete systems in the middle, and predictive hypotheses at the lowest level, which result from fitting models to data” (Forster, 2000, p. 233). He emphasized that “the essential point of this tripartite distinction is that predictive accuracy is a property of predictive hypotheses at the very bottom of the hierarchy, and is traded-off against the truth at the next level up—the level of models” (Forster, 2000, p. 233). In this way, both theories1 and models are tested by the utilization of tailored predictive hypotheses" (p. 300).
