I often hear behavior analysts comment that RFT is essentially the same thing as stimulus equivalence, or that RFT does not add anything new to the equivalence literature.
Here are a few points to help clarify the difference between RFT and stimulus equivalence:
1) Stimulus equivalence is an empirical phenomenon; RFT is a behavioral theory about how that phenomenon (and other phenomena) comes about. In other words, RFT provides an operant analysis of how/why people are able to form equivalence classes. I cringe when I hear behavior analysts try to use stimulus equivalence as an explanation for some other behavioral event without recognizing that equivalence itself is a behavioral event that requires a technical analysis! This is especially true because the phenomenon of equivalence doesn't readily make sense from a direct contingency analysis (i.e., the "derived" or "emergent" relations are interesting because they're somewhat unexpected based on the organism's history of reinforcement in the presence of the "equivalent" stimuli...that is why we call the relations "derived" or "emergent").
2) Murray Sidman, a pioneer in behavior analysis and stimulus equivalence research, provided some of the earliest behavioral accounts of stimulus equivalence. Sidman's approach, however, was/is primarily a descriptive one: "My own theorizing has been directed not so much at an explanation of equivalence relations but rather, at the formulation of a descriptive system -- a consistent, coherent, and parsimonious way of defining and talking about the observed phenomena" (Sidman, 1994). A precise, coherent description of an empirical phenomenon is important, but it is not the same as a functional, behavioral explanation. RFT attempts to offer such an explanation.
3) In my view, RFT is a more scientifically conservative way to account for equivalence (as compared to Sidman's approach) because it does not require any new behavioral principles at the level of process (in Chapter 2 of the RFT book, we do propose a new behavioral principle at the level of outcome, but that is simply due to the unusual effects we see from the transformation of stimulus functions). Sidman, on the other hand, suggests that equivalence is probably a basic stimulus function "not derivable from more fundamental processes." RFT claims that it IS derivable from more fundamental processes -- basically, a history of multiple-exemplar training and differential reinforcement for relational responding.
4) The terms RFT uses to describe equivalence and other derived stimulus relations (e.g., mutual entailment, combinatorial entailment, transformation of stimulus functions) are more general than the terms used by Sidman (e.g., reflexivity, symmetry, transitivity, etc.). RFT introduced these new terms so that we could have a language to talk about all different types of stimulus relations (bigger than, before-after, opposites, darker than, etc.). Sidman's terms were taken from mathematical set theory and apply to equivalence relations, but do not work for other types of stimulus relations. In other words, RFT folks did not create new terms just for the hell of it or just because they sounded kewl.
5) RFT, as suggested in point 4, also emphasizes research on types of derived stimulus relations other than equivalence. This is important because stimulus functions can be changed on the basis of these derived relations, and the functions will be changed differently based on different relations. It has been demonstrated many times now that stimulus functions can transfer between members of an equivalence class (i.e., if one stimulus becomes a conditioned reinforcer, other stimuli in the equivalence class may also become reinforcers). But it has also been demonstrated that a stimulus can acquire new functions on the basis of a derived relation other than equivalence to another stimulus. For example, if stimulus A is a conditioned reinforcer and the learner derives a relation of opposition between stimulus A and B, stimulus B is likely to acquire aversive functions (the stimulus functions are transformed on the basis of its derived relation to stimulus A). This has been demonstrated with quite a few different types of stimulus functions and with quite a few different types of relations. Many researchers studying derived relations focus on equivalence relations exclusively, but RFT suggests knowledge of these other types of relations and their impact on the psychological functions of stimuli is also vitally important to a comprehensive theory of language and cognition.