@chai2,
I don't like the term either, but not sure what age you are referring to as not using playdate - sadly my daughter had used the term playdate in pre-school so yes young children use that term.
Also unfortunately as we do not live close enought to schoolmates, we do have to set up "playdates" - they have a couple of friends in the neighborhood that do not require playdates - just the normal running over to see if they are home, but with classmates, it is needed if they want to see them outside of school hours.