Yes and no. I've never heard of someone trying to use PayPal to pay someone else, however we do have PayID which is linked to your phone number (I hate it, since you can plug anyone's number into the PayID system and see who owns it). This is free and instant, however you don't really pay businesses with this.

Paying businesses you can use EFTPOS which I believe is run by the central bank and has very low fees on debit cards, or the usual credit card networks/Apple Pay/gpay.