Yes, that's correct. "Du" is a form of address when you know someone very well. When you want to address someone you don't know that good you say "Sie".
Sie spielen. ( "you are playing" as well as the plural form "they are playing")
Theres this theory that says that p much all occidental lenguages come from a prehistoric civ called "hindo-european" and its thanks to them "Tu" or similars are ways of saying informal you and most possesives start with h, from the Habere