"Spanner" and "wrench" are words that can refer to the same tool, depending on which side of the Atlantic you're on. When used together, the words can refer to virtually any tool that Americans consider a wrench.
For Americans, the best-known example of a spanner wrench is the adjustable box wrench.
Wrenches and Spanners
A wrench is a type of lever. The force you exert on its handle is transferred to the jaws to develop the torque necessary to turn the items they grip.
A large variety of jaw designs exist, including serrated, box-style and pin-style wrenches. The main characteristic that distinguishes a spanner from another type of wrench, such as a hex or torx wrench, is that the jaws fit around the item being turned.
For Americans, the word "spanner" also includes the extra connotation that the jaws are adjustable.
Most toolboxes include an adjustable box wrench because it can fit a variety of nuts and bolt heads. It isn't always the best tool for the job because the jaws often don't grip tightly, and the head requires clearance.
A socket wrench or non-adjustable box wrench often works better. Monkey wrenches -- also called pipe wrenches -- resemble adjustable box wrenches and can develop impressive amounts of torque.
Because it has a serrated head that can grip and turn metal pipes, a pipe wrench is one tool no plumber would ever be without.