For me, too, a basement is a partial below ground space-- since my house is on a hill--on one side the basement has windows about 10 inches high-- and on the other side-- 24 inches high 5 little windows in all. but a cellar would not have windows, and might not even have a a paved floor. it might be modified too-- root cellar or coal cellar-- or wine cellar-- the last one might be quite elegant-- one neighbor made one-- with beautiful stone walls--(not concrete blocks walls like my basement).
Most house in this area have some sub structrure-- but a few are slab houses-- built on a slab of concrete- with no basement, cellar or even a crawl space-- my enclosed porch has a foundtion wall-- but it only goes 18inches into the ground-- I have a little door high up on the basement wall-- i can climb a ladder, and "crawl" (on hands and knees) into space under the porch--(i personal have never done it-- but ex has-- when adding wiring) since porch is electronics (computer and stereo stuff) room, and wires from equipement run in basement ceiling to various other rooms--
and an Attic is a the space just under the roof (on a house with peaked or hip, or mansard roof) a garret is the rooms- (if any) I have an attic-- but since it only has a ladder for access, and it not high enough to make into rooms, its just an attic. In my first house, the attic had 2 rooms with slanted walls/ceilings these were garret rooms--(knee walls came up to about 4 foot high-- and the attic had Cubby rooms-- as spoken of earlier in this thread.)
