Just adding to the replies above - I think you could see DBT as 'going on a course' where you have hired a tutor to teach you a specific set of skills and help you become good at them. A bit like learning to drive or learning a language.

CBT as I understand is also very goal-driven, but could be seen as more of a partnership with you and the T working out the problem, and then focussing on a specific solution to the problem.

That's just my idea, my T has explained these therapies to me and I've got a DBT workbook which I find helpful to have at home as a kind of self help book. But I haven't exactly done either of these two therapies. I've done schema therapy, which has elements of both I think, but it's a different therapy.