Buckets are usually taller and they are wide and include an attached swivel handle of some sort. Tubs are usually wider than they are tall and do not include a handle. In both cases the lids are separate pieces that can be removed. These lids usually have large studs resembling over-sized versions of the ones found on regular bricks. There are at least two different sizes of these studs that are not compatible and despite appearances these containers do not clutch as regular elements.
The buckets are often used by LEGO Users Groups as the base for signage or fences to control or inform the public at displays. Filled with sand or concrete the bucket can support a pole to which signs or fences or rope can be attached.