As for the write up I have,
QI Christmas Special
BBC1 10.35PM It's a laughing matter...
Stephen Fry joins the wit and wisdom of guests Dom Joly, Clive Anderson and Rob Brydon in this festive edition of the quiz.
Natalie: "Are you finished with your coffee cup Stephen?"
Stephen: "Yes Natalie darling I am, although it's not a coffee cup, it's a teacup..."
*5 minute debate later*
Result: The contents of the cup do not determine the name of the cup. The cup is a cup/mug whether it contains tea/coffee/ribena/hot chocolate or any other beverage.