Process: Process defines how a unit of work (a work item) moves until it is completed (resolved). In Pega, a business process corresponds to a flow rule, which is associated with a work item. A flow may define many optional detours, side trips, and branches reflecting decisions reached along the way. The path that one item follows through the flow depends on its own requirements, automatic decisions in rules, and on available resources. 

https://community.pega.com/process-overview/process-overview

Activity:In PEGA, an Activity is an instance of the Rule-Obj-Activity rule type. An activity is the fundamental sequential processing unit of the Process Commander system in PEGA

An activity when defined consists of a sequence of steps, each of which can contain a method or an instruction. 

https://community.pega.com/introduction-activities/introduction-activities

Hope this helps.