Catering: not a yes or no question
The problem is that the question has a false premise, the premise being that the question can be legitimately answered by a yes/no response. Only when you carefully define them in mathematical or scientific context do words have clear boundaries. Normal usage has gray areas.
So catering:
A> If a restaurant serves a meal to a customer who walks in as part of its daily business of menu service at tables, then that is not catering. Most native speakers of English would agree with that.
B> If a restaurant supplies food for a social event outside of its own walls, then that is catering. All native speakers who know the word would agree with that.
C> If a restaurant supplies food for an event (wedding, rehearsal dinner, graduation party) at its own location, and that food is served on buffet tables in a large room at the restaurant, but waiters/waitresses do not come to the tables to take food orders (although they might take orders for drinks), then many many native speakers would call that catering, but not all would.
D> If a restaurant supplies food for a social event at its own location (wedding, rehearsal dinner, graduation party), but waiters and waitresses come to the individual tables to take food and drink orders, then I think most native speakers would not call that catering, but some would.
In normal human use, words do not bear scientifically precise meanings. The field of "category theory," if I remember correctly, explores the fuzzy areas of those meanings. To demand a yes/no response is to demand an incomplete answer.