Just to throw it out there, 86 is also used in the film industry (at least in LA) meaning to cancel or get rid of something. It's very widely used across the industry. I don't know of any other slang that is shared between restaurants and film though.
Just an aside. I worked well over 20 years in food service as a second job. I don't think "86" is a widespread term in food service, there are some of us that would know what you meant, but not many. If I had to guess, I would guess its origins were with the Trucking industry, specifically CB/shortwave radio operators since they abbreviated a TON of phrases with numbers.
I was mostly curious and love random trivia. So I looked it up and apparently it has a wiki page. It did actually originate in the restaurant/bar scene but way back in the 1920’s.