There isn't single theory in the context of nomenclature - UX and UI started to differentiate in the industry - as occupations or scopes of activities.
However, the CX and BX context - may exist in a broader brand and marketing context.
CX - Customer Experience
Is how the client experience during a given process (e.g. purchasing a service, item, etc.)
That is, for example, defining touchpoints and examining reactions, feelings, emotions, conversion optimization.
Shops take care of all the senses (smell, sight, hearing)
UX - User Experience
How the user experience in a digital context - using a software product.
UI - User Interface
it's how the interface is designed (architecture, usability, interactions) - there is no reference here to behavioral psychology or cognitive science like in the UX case.
BX - Brand Experience
honestly - I hear the first, but by deduction I think it is the widest and associated with the brand in all circumstances (ads, references, reviews, image on the internet)
When it comes to scopes(there will be divergent opinions of course) - :
BX ∈ CX ∈ UX ∈ UI