Bobbi Hoadley

The short answer to this question is yes.  Applied Behaviour Analysis (ABA) and Cognitive Behavioural Therapy (CBT) are related. The difference between ABA and CBT is in the depth and types of services available. 

Both therapies are behavioural approaches that evolved in the 1960's as a result of advances in the research on human behaviour.  In the 1980's Cognitive Behaviour Therapy became popular because it was easy to use, solution-focused and there was evidence that it actually worked better than other psychotherapies. 

The evidence regarding all therapies based on behavioural science continues to grow. However, CBT was immediately accessible to consumers because it could be used by any counsellor or psychologist who was interested in learning about it. Though there is a credentialling process, it is not necessarily used or required.

ABA on the other hand, has over the last 20 years developed a rigorous process for ensuring a much more extensive knowledge base, technology, and standards for using it. ABA is also claimed by people who are not credentialed, but that is becoming much more difficult to do as time goes on.

The CBT approach addresses cognitions as a means to change behavior, and puts that together with simple behaviour change procedures as cognitions are modified.  I used it to efficiently recover from a phobia of airplanes when I was young.  It is, in my experience, very effective if the problem is understood, and if  the individual already has some insight into the behaviour.  

The ABA approach analyses behaviour (including cognitive behaviour) to identify the underlying function of the behaviour so we know what will work before we do anything.  We then choose from a vast technology of behavioural approaches and keep data on each intervention's success to ensure effective, efficient and reliable progress.

Some people do not respond to traditional therapies including CBT, for a world of reasons, each personality is unique. Additionally, if a behaviour is complex or resistant to change, if an individual's brain function is compromised, or if they are missing some of the behaviours foundational to insight, Applied Behaviour Analysis has better data on effectiveness. Additionally ABA is preferred by people who are tired of talking about their issues and getting nowhere. 

There's more information on Cognitive Behaviour Therapy or CBT here