I've never heard that definition or distinction. What about walk-out basements? There is often access from the inside as well as the outside of the house.
Walk out basements are basements with a door walk-out that does not have stairs to enter or exist the basement.
“Cellar” is a rather old term, and typically applies to much older homes that had a space below the house in the ground, and was entered from the outside the house. Typically had two slanted swing open doors revealing the stairs….and many times had dirt floors, and often was used as a tornado / storm shelter and root cellar. Nothing like modern finished (flooring, nice wall covering, and finished ceilings) actually expanding the “living’ space….bedrooms, family rooms, game rooms, bath room, laundry room…etc…without enlarging the foot-print of the actual house foundation.