Cluster is a special case of distributed system. The defining feature of a cluster is tight coupling between computers in the system, which are, in case of a cluster, typically located next to each other and connected via high-speed network.
hamster143 is right. A cluster-based system is an example of distributing computing. Clusters can be many CPUs linked together in the same, single room. In fact, supercomputers are not always single monolithic machines anymore; the fastest supercomputer in the world is a Cray-built cluster located at Oak Ridge National Labs in Knoxville, Tennessee, USA. (While the term beowulf was once used to describe clusters, it is no longer in use.) Cluster-based systems are used for large computations for applications in physics, finance, engineering, and other compute-intensive areas.
However distributed computing can also be less compute-intensive, with no need for the speed of a supercomputer, and spread out over many different machines in many locales. If a point of sale machine at a restaurant needed to upload a customer order to a database stored on a central database while other machines across the country are doing the same thing at the same time, a distributed software program could accomplish this.