Okay, children, settle down.
'Broadway' refers to the size of the theatre, not the address. 'Broadway theatres' are houses with over 500 seats. All of the theatres are in Manhattan, most of the theatres are located between West 41st Street and West 52nd Street, between Sixth and Ninth Avenues, although the Vivian Beaumont in Lincoln Center is considered a 'Broadway' theatre. Only the Winter Garden, Marquis, and Broadway are physically located on Broadway, the street. Most are on the side streets.
Off-Broadway theatres are houses with 100-499 seats. They are located all over Manhattan, generally south of 86th Street.
Off-Off-Broadway theatres are houses with less than 100 seats. These 'theatres' can be anything from a loft to a basement, and are also located all over Manhattan.
I am not a theatre professioanl so I can't address the Actors Equity rules and regulations but I though I would at least explain the difference in the types of theatres, as I understand it.
'Our whole family shouts. It comes from us livin' so close to the railroad tracks'