Specific terms for the tray and the bus-like cart used by vendors in theaters, stadiums, trains, etc
A flight attendant is said to push a beverage cart.
A peanut or pretzel (or cigarette) hawker at a stadium is said to carry a vending tray
Maybe you're looking for vending cart or vending tray. I don't know of any word that encompasses both.
On the UK railways, the phrase "trolley service" is used to describe food and drinks sold by an employee walking along the train. The items are sold from a trolley. The same term is used for the airline equivalent, hence the dated/sexist "trolley dolly".