I think the confusion is between "full balance" and "statement balance." The statement balance will generally be lower than the full balance, since the due date is typically weeks after the statement closes.
Exactly; it's effectively the same thing but with a rolling one-month interest-free float.
I think you're probably right. I pay/autopay the statement balance by the due date but I don't send the CC company money that isn't actually due yet even though it's already on the card.
Ah this helps! Yes I pay my full statement balance on the due date (in most cases.)