(Actually, around my way virtually no one has such a thing inasmuch as the houses are all built on hardened lava. Topsoil is pretty damn thin. You hit bedrock almost immediately.)
In the New England idiom there's a very subtle difference between 'cellar' and 'basement.' Houses, i.e. private homes, are generally said to have 'cellars.' But if you go into a public building, e.g. a store or office building, there are no cellars -- there may, however, be some facilities that are located at the 'basement' level. And, speaking of facilities, when I was in the fifth or sixth grade (form), the school in the Jamaica Plain section of Boston was a big red brick building, dating to the 1880s. (It has since been razed and a small playground opened on the site.) The 'facilities', i.e. rest rooms, were all in the basement. If you had to go, you ddidn't ask the teacher for permission to go to the boy's room or the bath room or the rest room. You said you had to go to the basement and that was immediately understood.
