An outbuilding is a general term for any separate smaller building on the same property as a main house. A shed is a specific type of outbuilding, usually a simple structure for storing tools or equipment. An annexe (or annex) is an extension or addition to a building, often connected by a passageway — unlike an outbuilding, it is not fully separate. In modern usage, an outhouse refers specifically to an outdoor toilet, while outbuilding carries no such association. If you are describing a separate structure used for any purpose — garage, workshop, barn, or studio — outbuilding is the safest and most neutral choice.
From out- (prefix meaning 'outside, external') combined with building. First recorded in English in the early 17th century, it originally referred to any structure built outside the main dwelling on a property.