"Premises" is a general word which means the building and the land the building is on. "Facility" is a general word which describes a certain kind of building which serves a particular purpose. Let's invent a story. There is a group of buildings on a piece of property which is owned by a manufacturing company. One of the employees has a heart attack and needs help. They make an announcement over the loudspeakers "is there a doctor on the premises? We need help in the packaging facility!". The announcement is asking if there is a doctor in any of the other buildings or on the property owned by the company. They are asking the doctor to go to a specific building which is the packaging facility. Not a very good story, but you get the idea I think.