I think the way many people understand retrograde motion from hearing about it is a bit simplifeid and misunderstandable which is why a full 2d visual representation can be so helpful
it's not just that "earth overtakes mars because its moving faster so mars seems to move backwards" - earth is always faster tha nmars so if it was that simple mars would always seem to move backwards and we would call that forwards
it's that when they're on opposite/relatively far offset sides fo the sun the earths movement and the movement of mars itself both make mars appear to move "clockwise"/"eastwards" against hte background stars as seen from earth and add up, its only when they are close to each other in that moment of overtkaing that the earths movement makes mars appear to move "coutnerclockwise"/"westwards" and since iti s faster than mars own movement this makes mars appear to move opposite for as long as the angle is right for the actual appearent motion from earths movement to be more relevant