Perhaps the first one Chapel inserts is a generic "I'm crew, gimme food" clearance card
I really do thing that is all they were. And the individual square didn't have anything to do with a certain dish, they just gave you access to the system.
What Christine was doing was play a game with the children, if Christine had had only one square left and Mister Picky had made his elaborate request, she would have assured him that the one square she had left would have been the right one. She gave him a alternate square because she had another square left over.
When Kirk (in The Trouble with Tribbles) inserted his yellow square into the "food slot machine" what happened? He didn't seem to order anything, verbal or by buttons, but he knew that his tray was supposed to hold a chicken sandwich and coffee. One possibility is that he returned to his quarters and retrieved the correct square from his meal square collection. Or, that was simply the only thing on the lunch menu that day, no choices. Or, in some way Kirk made a deliberate selection at the time.
We just didn't witness it happening.