A dry pail is an empty bucket or basket used to store dirty nappies until wash day. The ideal dry pail allows for lots of airflow, which minimises smells. A washing basket with holes in the side is perfect.
Decades ago wet pailing was the most common method of dirty nappy storage. This is no longer a suitable or needed option. Napisan previously contained sodium hypochlorite (the active ingredient in bleach which sanitises), it no longer does, so the modern Napisan/Vanish does not sanitise. Wet pailing poses a drowning risk, creates a perfect breeding ground for bacteria to flourish, constant soaking of nappies degrades them prematurely and is more labour intensive.
Wet bags are water resistant bags made of PUL, which can be used for storing soiled nappies while out. They are also useful for wet swim wear and clothing.