Both radars display the exact same scenario. One radar is in North-Up mode and the other in Head-Up mode.
When your Own Ship changes course in North-Up mode, the heading marker moves and the targets remain stable.
When your Own Ship changes course in Head-Up mode, the heading marker stays at 000 relative and the targets arc across the screen.
It is good to be comfortable with Heads-Up mode because a North-Up radar will default to Head-Up if it loses Own Ship course data.