Use the Assignment Service shape in a flow to pass control to an external system using a connector (for example, Connect BPEL rule). Assignment Service shapes support asynchronous coordination with external systems.
Both Integrator shapes and Assignment Service shapes reference an activity of type Connect. For an Integrator shape, flow execution continues as soon as the activity completes. For an Assignment Service shape, flow execution pauses until PRPC receives a incoming service request of the appropriate type.
If I am correct, the synchronous and asynchronous part is taken care in the activity itself through "Run" or "Run in parallel" and then using connect wait method. Then how does this flow shape impact that configuration.
Also what would difference if I call the same activity through Integrator shape and this assignment service shape apart from synchronous thing that you mentioned above.