Bathrooms are called by many names around the world. Even in the English language, there are several terms used to describe the same room. Lavatory and water closet are terms often used interchangeably, but their origins and the specific uses of the terms differ somewhat. The difference is primarily an etymological one, as inside the room they refer to essentially the same thing.
The word lavatory has its origins in Latin. In Latin, "Lavare" meant to wash; over the years, the word went through a number of changes that resulted in the term lavatory indicating a room where washing of a person was done. In the 19th century, the term began to apply to rooms that contained toilets, which is how the word has come to be used in the 21st century.
The origin of the term water closet stems from an invention that was made for Queen Elizabeth I. Her grandson, John Harrington, invented a type of indoor flush toilet that used water to carry away waste. Because water needed to be accessible from the device to remove waste to the sewer system and because the system was designed to be put into its own small dedicated room, he named the invention the water closet.
Current Use - Lavatory
Some people still use the term when referring to a bathroom. Its use is near universal in the transit industry. On airplanes especially, the restroom is almost always referred to as the lavatory. This carries over to other aspects of the transit industry, as well. Trains and buses sometimes also refer to the bathroom as the lavatory.
Current Use - Water Closet
Water closet is a term used to refer to a bathroom in many parts of the world. Sometimes, a washroom is marked simply with the initials "W.C." to signify the purpose of the room. These initials are also used extensively in countries where English is not the primary language to signify to English-speaking travelers and tourists where the facilities are located.