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Both the modes work on request response model but the actual implementation differs, so the requests sent by clients should be different in each case.

RPC mode is implemented using TIBCO Adapter SDK's RpcServer endpoint while Request/Reply mode is  implemented using a Subscriber endpoint.

"Publish to adapter" activity must be used for sending request when the adapter service is configured in the Request/Reply mode  while "Invoke an Adapter R/R Service" activity can be used for RPC mode.
Both these activities belong to the ActiveEnterprise palette of BW.