A bucket is usually an open-top container. In contrast, a pail can have a top or lid and is a shipping container. In common usage, the two terms are often used interchangeably. A trolley is an object with wheels that you use to transport heavy things such as shopping or luggage.
 
A mop bucket cart trolley is a wheeled bucket that allows its user to wring out a wet mop without getting the hands dirty. The cart has two buckets with the upper one usually clipped onto the lower.
 
Mop buckets hold water and chemicals for cleaning floors. Sometimes called mop pails, they have handles to make it easier to transport and maneuver. Some of them use steel material to prevent rust and handle added pressure. There are also plastic buckets that offer lightweight durability.