My interpretation of "bar food" is heavy American food; burgers, fries, chicken wings, etc. This is food that is commonly served in bars/pubs in the US.
Bar snacks, on the other hand, brings to mind the bowls of peanuts or other salty food in the counter of a bar; generally used to make people thirsty and purchase more alcohol. From a description of 아주 in one of the other comments, this is much closer to what it means in Korea.
It's hard even to interpret it as Korea doesn't really have "bars" per say. Most places that serve 안주 don't serve any food except 안주, so you don't really have a choice between bar food and bar snacks. Plus things like 심치전 or soups are common 안주 and those are a lot heavier than snacks