Earlier quoted context omitted.
As it says in the title, it's more anonymous. So ZCash and Monero are competing for the darknet payment market.
But it can't really be truly anonymous, not if you want people to actually use it. At the end of the day you need at least some assurance that you're sending the money to the right person in exchange for their good or service. They also need to be able to verify that they have been paid for their work and by whom.
Now imagine that the restaurant didn't possess any information that it could use to identify you as a result of the payment, and that no payment intermediary possessed information that could be used to identify the parties to the transaction, and that when the restaurant later spent the money, the source of the funds couldn't be associated with your payment transaction (perhaps even by you as the customer).
Those are some properties that we could wish for in an anonymous payment system. It doesn't mean that the payee can't tell that a payment was made in response to a particular request, though it might not know "by whom" in any other sense.