I just sold my house and bought a townhome where I don't have to mow the lawn, shovel snow or repaint the garage doors.
This made me think about unique US architectural terms. My old house was a tri-level, one form of split-level architecture largely inspired by Frank Lloyd Wright. The new townhouse says it has an open floor-plan, currently a popular architectural feature. The tri-level made excellent use of what you would call "shared air space", though not in the same way an open floor-plan does.
People buying and selling homes in the US suburban sprawl use these terms. How about other countries? As a traveler, I'm usually in the heart of cities! I did first learn the concept of a residential condominium decades ago when I went to France. I need to ask my students about the words they encounter when looking for housing.