Annex, extension, wing and ell designate an addition to a main (and, often, the original) building.
An annex may be attached to the main building or it may even not be adjacent to it. When used of an addition to a hotel, an office building, or a commercial or educational establishment it usually implies a provision for expanded activity.
An extension is attached to a main or central building; when it projects from the central building and is connected with it at only one point it is called a wing; when it extends at right angles from one end of the building it is called an ell.