It is an acronym for Space Transportation System (STS). you are correct in that each flight of the shuttle has this in the flight number.
I was at the Johnson Space center in Houston a couple of years back, and while touring mission control, you can see a plaque that bears the mission number of each spaceflight. Each crew has a hand in the design of their plaque to commemorate their particular spaceflight.
It was surprising to me how small mission control actually is.
By the hollywood standard, you think it is a HUGE room with people running everywhere, but in reality, it is like a very small theatre, like maybe 50 feet wide or so, with several VERY large computer screens at the front of the room mounted up high.
They run training simulations all the time when there isn't an active mission up. It's a cool place to visit, if you ever get to Houston and have a free afternoon, i highly recommend it.