To complete a request essentially means you are just removing that request from your work queue. It is a private action that only you can see was done. It does NOT update the status of a request or send any message to your ILL partner on the request, so if a request was "pending" or "in process" before you completed it, it will stay that way after you complete it! It is best to complete only those requests that have been "returned", terminated, or those that are in your Idle or End of Rota queues.
When you cancel a request, you send a cancellation request to the current lender in the request's rota. When that cancellation goes through, then the request will go to the next lender in the rota.
When you terminate a request, a cancellation request goes to the current lender AND VDX stops the request from moving to other lenders. Then the request will move to your "Terminated" queue and will be marked with the message, "Request No Longer Required."