I don’t think of it as a difference from the English word “cuisine” at all. We probably both agree on what constitutes Mexican cuisine, more or less, but differ on why Mexican cuisine is being mentioned in the context of a supermarket. Can cuisine=mexican only mean “serves food from Mexican cuisine”, or can it more broadly mean “known for facilitating Mexican cuisine”?
In linguistic terms, our key names introduce the comment but only imply the comment’s relationship to the topic (the feature). In other words, we lack true predicates. The few predicate-like keys that have been proposed end up looking out of place, such as is_sidepath:of. This predicate-less design enables iterative refinement but creates a lot of opportunities for misunderstanding.
I’d contend that the distinction between “serves food from a cuisine” and “caters to a cuisine” doesn’t really matter that much. If you search for supermarkets in Chicago and one of the results is labeled “Mexican”, you can safely assume that the supermarket carries fresh tortillas and pan dulce, even if both were made just steps away in the back of the store, well within the United States. I may buy bell peppers there for an Asian stir fry instead of for fajitas, but what difference does it make to the store’s overall character?