Final answer:
A mezzanine is a partial story between two main stories in a building, often projecting as a balcony and working in composition with the story beneath. While 'clerestory' pertains to windows for light, a 'bay' defines space between structural elements.
Step-by-step explanation:
The architectural term for a low or partial story between two main stories of a building, especially one that projects as a balcony and forms a composition with the story beneath it, is known as a mezzanine. A mezzanine is often used to provide extra space for a variety of purposes, such as a lounge, additional offices, or a seating area. It can be seen in various building types including theaters, commercial buildings, and residential structures.
The term clerestory refers to an upper level of windows that admits light into the central space of a building, which is distinct from a mezzanine. Moreover, a bay is a division of a building defined by vertical elements like columns, but not necessarily representing an intermediate level within a story.