You appear to be falling into two common traps here. The first is to assume that REBT is not CBT, and the second is to think that Ellis' and Beck's methods differ mainly in the style of therapist.

REBT is not different to CBT - it is CBT! So is CT (Beck's 'Cognitive Therapy'). CBT is a generic term for a category - there are many different types of CBT. REBT & CT are the two main types, but there are many others (such as DBT, Schema Therapy, etc).

As I have written elsewhere in this forum (see the link in Jim's earlier message), Ellis & Beck have different styles, but these are typical of the particular therapists - not of the therapies they founded. Both REBT and CT can be conducted aggressively or gently. Ellis is fairly directive in his approach, but many REBT therapists (myself included) are more 'Socratic' (questioning).

Finally, you are correct in saying that REBT & CT are very similar. I think the main differences are in the terminology used; though one key difference between the two is the type of thinking that is the main focus of attention: CT seems to focus mainly on inferential-type thinking (e.g. 'I am always failing'); whereas REBT emphases a focus on evaluative thinking (e.g. 'Failing so much is unbearable / proves I am a failure as a person / should not be happening'). Note that both methods work!

Hope this helps to clarify your question.