The therapeutic brands are misleading as there’s a lot of overlap in techniques.
I quite like this simple table from Mick Power (2010, p. 49) of the different techniques, expressed in a cross-modal way.
Power argues that
“… therapy heightens access to cognitive–emotional structures and processes that relate to past and present significant objects and significant others including the therapist. In the context of this heightened access, there is the common therapeutic goal that patients will relearn, cope more successfully with, view more realistically, reinterpret or reconstruct; that is, in some way view more constructively the object, person or situation that has been the source of their distress or conflict.”
Fonagy and Bateman (2006, p. 425) go somewhere similar with the interrelationship part of this:
“It is possible that psychotherapy in general is effective because it arouses the attachment system at the same time it applies interpersonal demands (psychotherapy technique), which require the patient to mentalize, to confront and experience negative affect, and to confront and review issues of morality (superego). Why might this be helpful? We speculate that thinking about feelings, thoughts, and beliefs in the context of attachment is helpful because in this “paradoxical” brain state there may be more access to modifying preset ways of conceptualizing the contents of one’s own and other’s minds, as well as issues of morality and social judgment. Activating the attachment system harnesses brain biological processes partially to remove the dominance of constraints on the present from the past (long-term memory) and creates the possibility of rethinking, reconfiguring intersubjective relationship networks.”
Fonagy, P., & Bateman, A. W. (2006). Mechanisms of change in mentalization‐based treatment of BPD. Journal of Clinical Psychology, 62, 411-430.
Power, M. (2010). Emotion-focused cognitive therapy. London: Wiley