I used to think that together with a date they identified a flight, yet tomorrow at 00:20Z AA46 flies ORD-LHR, and then later tomorrow, at 23:15Z, AA46 does the same trip.
You are almost correct. The combination of a flight number, airport of departure and date (both local and UTC) is supposed to be unique.
If a flight is scheduled to depart twice from the same airport on the same Zulu day, then one of the flights will be identified with a Z suffix on the flight number (not normally shown on flight information displays).