Room, berth, play, elbowroom, leeway, margin, clearance can all mean enough space or scope for free movement.
Room, the general term, often means sufficient or ample space for doing something (as working, growing or developing, sitting, passing, or entering or leaving).
But the word may also mean an occasion, an opportunity, or an opening that admits or permits something.
Berth, basically a nautical term meaning maneuvering space for a ship, in more general use denotes a space kept between one and some source of potential danger.
Play (see also PLAY FUN ) can specifically imply freedom of movement and action especially with reference to two or more things which must work together in close relation or without interference or conflict.
Elbowroom does not greatly differ from room except that it is somewhat more forceful and definitely implies freedom from interference or constraint as well as space for movement or for action.
Leeway, basically a nautical term meaning the drift to leeward especially of a sailing vessel, in its closest extended sense means a falling off from the line of progress and therefore may connote something (as a shortage) to be made up.
More frequently, however, leeway tends to mean room or margin for freedom of action.
Margin (see also BORDER ) implies an amount (as of time, money, or material) additionally allowed or made available so as to provide for contingencies or emergencies which cannot be foreseen.
Clearance stresses lack of obstruction. Typically it implies a carefully calculated amount of space between two physical objects such as the water level and the underside of a bridge, or a roadway and the underside of a viaduct above it, or a shaft and the hole into which it is fitted easily but not loosely.
Sometimes it may apply to intangible obstructions and then stress removal (as by the satisfying of legal or official requirements) rather than planned avoidance.