Taking a shot at this, one concrete definition might be that the business model is essentially white labeling, that is, the base LLM is rebranded, but task performance in the problem domain is not functionally improved in some measurable way. As a corollary, it means the user could receive the same value if they had gone straight to the base LLM provider.

I think this might be more narrow than most uses of the term “wrapper” though.