Distributed computing can be defined as a method of information processing in which work is performed by separate computers linked through a communications network.
Parallel Computing or Programming is the splitting of a single problem into a number of subtasks that can be computed relatively independantly and then aggregated to form a single coherent solution.
Parallel Programming is most often used for tasks that can easily broken down into independant tasks such as purely mathematical problems e.g. factorisation.
Problems such as these are known to be 'embarrassingly parallel'.