Database Clustering is actually a mode of synchronous replication between two or possibly more nodes with an added functionality of fault tolerance added to your system, and that too in a shared nothing architecture. By shared nothing it means that the individual nodes actually don't share any physical resources like disk or memory.
As far as keeping the data synchronized is concerned, there is a management server to which all the data nodes are connected along with the SQL node to achieve this(talking specifically about MySQL).
Now about the differences: load balancing is just one result that could be achieved through clustering, the others include high availability, scalability and fault tolerance.