Attic can never be referred to when speaking about the basement. The basement is downstairs (underground level of a house). The attic is upstairs (usually last level of a house before the roof). Yes, an attic is most commonly used for storage. But in the US, we typically store our "stuff" in the garage ;)))

You’re right, it’s the space between the ceiling of the upper floor and the roof of a house. If it has flooring and maybe a window, and gets used as a room it might be called an attic room, a loft or a loft conversion. In most houses (I think) in the UK it’s just used for storage and often has no flooring. The basement is just the basement, or cellar, in the UK, it can’t be referred to as the attic.