An appetizing store, typically in reference to Jewish cuisine, is best understood as a store that sells "the foods one eats with bagels."
"Appetizing" is used as a noun by itself to refer to the type of foods. Appetizing includes both dairy and "parve" (neither dairy nor meat) food items such as lox (smoked salmon), whitefish, and cream cheese spreads. The foods are typically eaten for breakfast or lunch and, based on Jewish kashrut dietary laws, include no meat products (kosher fish products are not considered meat).
The simplest distinction is that an appetizing store is a place that sells fish and dairy products, whereas a delicatessen sells meats (but not any dairy products, if it is a kosher deli).
The term is used typically among American Jews, especially those in the New York City area, where "appetizing shops" sell cooked fish and dairy products in some neighborhoods with large Jewish populations.Pareve and dairy restaurants in Toronto also have "appetizers" as part of their name that are both kosher and kosher style.
Also, it can be called 'appy table', 'appetizing table', or just 'appy', the last short for 'an appetizing store' or 'appetizing' in the way deli is short for delicatessen (the meat or the store).