Four-wheel drive, 4WD, 4x4 ("four by four"), all wheel drive, and AWD are terms used to describe a four-wheeled vehicle with a drivetrain that allows all four wheels to receive power from the engine simultaneously. While many people think exclusively of off-road vehicles, powering all four wheels provides better control on slick ice and is an important part of rally racing on mostly-paved roads.
Four-wheel drive (4WD or 4x4 for short) was the original term, often used to describe truck-like vehicles that required the driver to manually switch between a two wheel drive mode for streets and a four-wheel drive mode for low traction conditions such as ice, mud, or loose gravel. The "all wheel drive" term (AWD for short) was invented to distinguish vehicles that are capable of driving all four wheels on normal roads without causing poor control and excessive tire and drivetrain wear. The AWD term is now being used to market vehicles which continuously drive all four wheels, but it is just a marketing term. They are just derivatives of 4WD systems. The terms are thus quite vague in modern usage.
The buyer must be wary. It is common for identical drivetrain systems to be marketed under different names for upmarket and downmarket branding, and also common for very different drivetrain systems to be marketed under the same name for brand uniformity. For example, both Quattro and 4motion can mean either an automatically engaging system with a Haldex clutch or a continuously operating system with a Torsen differential.