Cloud computing is a business model for distributed computing, parallel processing can be done on cloud. High performance computing can be achived using parallel processing over cloud. Basically, we divide the computation task interms of smaller independent chunks called cloudlets and sent over cloud systems for processing them parallel, result will be accumulated and present to client, this is what parallel processing over cloud.
As long as you are able to use the resources to execute several tasks in parallel it is paralle processing. Cloudlets can play key roles here.
parallel processing is the processing of program instructions by dividing them among multiple processors with the objective of running a program in less time
http://searchdatacenter.techtarget.com/definition/parallel-processing
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