A train service can be identified by the train company, the date and a train number. This should not be confused with the number(s) of the vehicle(s). There are often several train services on a day with the same physical train. On the other hand, the train service of the next day with the same number may be carried out with other vehicles.
Similarly a flight service can be identified by the airline company, the date and a flight number. This should not be confused with the tail number of the airplane. There are often several flights on a day with the same airplane. On the other hand, the flight of the next day with the same number may be carried out with another plane.
The same applies for other public transport.
A flight number is more often relevant for the passenger than a train number: although the latter are usually in the time-tables, they are often ignored, because most people find it more practical to identify train services by route and departure time.
In the US air crashes are often referred to by their flight number. Elsewhere they are usually referred to by the name of the location of the crash, e.g. Lockerbie.
See also Airline call sign.