What do you mean by "If the train number doesnt have 'S', then it would be updated accordingly. "??
In the initial days, 'S' was used to denote one day special trains, which was run as an introductory train for a single day before the official launch/runnings of new trains.
Later 'S' was used to denote all the trains which had a specified...
more... last day of run; i.e. train running for one day, two days or thrice and ultimately losing its existence.
This is why the trains are now referred to as 'Intr (Introductory) Specials.