Two flights to the same place by the same aircraft on the same day will always have different flight numbers.

Airlines often do this for short trips e.g. London - Paris. The same aircraft (and crew) may do all the flights back and forth for a given day.

To allocate seats, the system needs to know the specific aircraft, as seating plans on aircraft can be changed easily (and sometimes frequently). Even 2 aircraft of exactly the same model may have different seating arrangements.

I too am very surprised that the passenger booked on the later flight was able to board. It might be a broken data model, or the person checking maybe ignored a warning, but either way it is a significant security failure.