You don't have to pay the Apple card balance in full to pay no interest. You just have to make the payments on the agreed-upon schedule. You're effectively doing something like splitting a $1200 purchase into 12 $100 payments or whatever, rather than that plus interest. No credit card I'm aware of will do that for purchases in general, but presumably it's worth it for a card issued by the actual product vendor if it increases sales. They have enough cash on hand that it hurts them none to receive most of the payment in the future.
PayPal has an interest-free credit option, usually spread out over six months, as well. You don't always have to make a specific payment on the due date, but if you don't pay it off in six months then the whole amount of accrued interest is due.
No. The financing Apple is offering is typically 12 months split into 12 separate payments. That is 0% financing and not a 'charge card' style. You're still getting 11 months of delayed payments, unlike a charge card where everything is due once a month from the previous month of the card.