If RAT is deployed manually from EMER ELEC PWR panel then it will pressurize the Blue Hyd system. Blue system will then power a hydraulic motor which runs the Emergency generator. There is a valve which opens and lets blue hydraulic to power the motor (Supply hydraulic power to CSM/G) if RAT is selected from EMER ELEC PWR panel. Also GCU will close the emergency generator line contactor if RAT is selected from EMER ELEC PWR panel (There is also AUTO logic for this). Selecting RAT Man ON on HYD panel will only deploy the RAT and pressurize the blue hyd system. It will not open the valve for the motor nor will the GCU close the line contactor. Hence on the HYD panel it says RAT MAN ON whereas on EMER ELEC PWR panel it says RAT & EMER GEN MAN ON (Auto).
Ref : FCOM DSC-24-10-30-30 EMER GEN Running.