Ideally they should be different, but generally speaking the ROS is information obtained from the patient. The objective findings noted in the exam are the provider's findings. They may match up, they may not.
It's entirely possible that the provider asks "Any mood swings, anxiety, trouble sleeping, or racing thoughts?" To which the patient replies "No." So the provider writes down "Psych: stable" in the ROS. On his exam, he/she may note that the patient is alert, responding appropriately, seems to speak well, shows good judgement, etc. So that may explain the "Psych: stable" note on the exam as well.
I wouldn't just arbitrarily decide that since he/she used the same verbage, it must be thrown out. I would however use it as an opportunity to talk to the provider about stating negative findings (no mood swings, no SI/HI) whenever possible.