Behaviorism in its original form assumed that thoughts or emotions don't exist, or at least that it is unscientific to talk about them. Later behaviorists took less extreme positions, and allowed "black boxes" in their models corresponding to things that can't be measured (before inventing EEG).

In CBT the "B" stands for behavioral, but "C" stands for cognitive, which is like the exact of behaviorism. CBT is partially based on behaviorism, but the other essential root is so-called Rational Therapy. (Fun fact for LW readers: the Rational Therapy was inspired by Alfred "the map is not the territory" Korzybski. It's a small world.)

CBT has many parts like the acceptance paradox that have nothing to do with behaviorism.