Yes they do. However, one trip when I booked 3 rooms using my annual pass, all 10 room keys said adult, including my two young daughters. Either it was a mistake by the WL CM or a special thing because I had the annual pass..
I can only find one from last year's trip, my wife's key, and in bold capital letters it says "ADULT" on it, which would lead me to believe that my son's card probably said "CHILD."
They used to just say "Adult" and "Child" with the name of the person who reserved the room.
About two years ago, in addition to the "Adult" and "Child" they began adding names. Each person in the room will be given a card with their name as well as identifying if they are an adult or child.