Both are defined to be a set of computers that work together and give the end users a perception of a single computer running behind it.
So what is the difference here?
What is the difference between a car and a sports car? A cluster is a system, usually managed by a single company. Clusters have normally a very low latency and consist of server hardware. A distributed system can be anything. Having JS on the client and PHP-server code which makes up together a system is already called a distributed system by some people.
In general when working with distributed systems you work a lot with long latencies and unexpected failures (like mentioned in p2p systems). When building a cluster (or a big cluster which can be called supercomputer) you try to prevent it by using more robust hardware and better network interconnection (InfiniBand). But nevertheless, a cluster is still a distributed system. (A sports car still has 4 wheels and an engine)