This can be generally referred to as a distributed computing or distributed data processing. Some degree of distributed processing goes on in any computer system even on single-processor computers where the central processing unit (CPU) and input/output (I/O) function are separated and overlapped. This separation and overlap can be considered as one form of distributed processing.
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Generally we can say that a distributed computing system is a collection of autonomous processing elements that are interconnected by a computer network. The elements cooperate in order to perform the assigned task.
Here in distributed processing, we are distributing the processing logic. The definition itself says that processing logic or processing elements are distributed to get things done.