Ok, maybe there isn't, what is clear is we are all unclear about whether there is a Cog Therapy separate from Beck. What we were reminded in this thread that Beck created a cognitive theory to test psychoanalytic theory. The wave narrative goes from purely behavioral therapies to classic cognitive behavior therapy to third wave approaches like ACT, DBT, and others. So there doesn't need to be a cognitive therapy outside of Beck, like I said, he and others brought cognitive, social, and emotional principles into behavioral conceptualizations that radical behaviorists claim was a mistake.
My original point in all of this is criticizing the position of a group of ACT supporters and radical behaviorists that ACT techniques are purely behavioral and are not cognitive as well as the position that ACT is an entirely different approach that classic CBT. I think I challenged those points pretty well earlier before we got caught up in the weeds.
Also, my SN in conkey, it refers to the imaginary hand puppet friend of the character Bubbles from trailer park boys. Put some respek on it.