This is a question that often crops up - from students, from clients, from interested outsiders, from people interviewing me for jobs - and I want to give an answer that's both comprehensive and easy. It's up to you to decide how far I succeed!
What you see a lot of, these days, is people using the term 'CBT' as though it were the name of a specific therapy, and often confusing it with Beck's CT. I attended a talk, at the 2006 BABCP Conference in Warwick, in which the speakers described their research into childhood OCD. They said they'd compared CBT with Exposure and Response Prevention. Now that's pretty weird, given that Exposure and Response Prevention is a CBT. But what they meant (it transpired) was that they were comparing Beck's CT with Exposure and Response Prevention. These were well-qualified therapists, doing cutting-edge research, and yet they had been sucked into this terminological confusion.
It's pretty much the definition of what a therapy is (any therapy - including EST, Reichian Therapy, Analytical Psychotherapy, yada yada) that it seeks to replace an unwanted response with a preferred response. Like, if every time I see a worm I shriek and feel nauseous, the purpose of therapy is to change that reaction in some way, such that when I see a worm I stay calm. So what distinguishes CBT from other therapy models?
CBT, I argue, isn't a therapy; it's the umbrella term for a host of therapeutic methods. It includes Stress Inoculation, REBT, Exposure Therapy, Attribution Training, Self-Control methods, Beck's CT, and lots, lots more. On the whole we can categorise the CBTs into CTs and BTs, though any given implementation is likely to have fuzzier edges than that might suggest. For instance: are behavioural experiments a BT or a CT? I'd come down on the side of them being a CT, as they are meant to be persuasive. But opinions differ.
For me, the single concept that unites all of these CB Therapies is retraining. What we are doing is identifying unhelpful habitual responses, and teaching our clients how to retrain themselves out of those responses. In doing this they may exploit (under our guidance) a variety of psychological effects such as dissonance, habituation, overlearning, reciprocal inhibition, response competition and so on. So, exposure therapy retrains a certain visceral reaction, what we call arousal, exploiting the effect we call habituation. Or, practice of disputing irrational beliefs means practising a helpful cognitive habit (and, in Vivid REBT, forging an associative link between the unwanted emotion and the rational self-talk), which is a response that's incompatible with the original, harmful, response; so we're exploiting response competition and overlearning.
This is very different from behaviour modification. In BM the therapist is trying to modify the client's behavioural responses by manipulating the contingencies of their behaviour. For instance: if a child gets a hug every time it interrupts its parent, that's a contingency (if interrupts, then hugged). This is likely to result in a high level of parent-interrupting by the child. BM would look to change that contingency (to - perhaps - if interrupts, then ignored). Behavioural psychotherapy, on the other hand, involves instructing the client how to change their behaviour in order to alter their habitual responses, whether they be behavioural, cognitive or physiological.