Space: Place, having more or less extension; room.
Room: Unobstructed space; space which may be occupied by or devoted to any object (…)
The general guiding his troops wants space to manoeuvre, but most people want room, breathing room. There's no space for a new file on my hard disk, but no room for a new book on my shelves. Maybe there's room for argument here. (Are my examples idiomatic? I am not a native English speaker.)
What guides the choice between room and space in this sense? Are there other words to consider (such as place, which I would have thought to be a Gallicism)?