Yes, residency discount is available for some routes. When you're making your booking online, if discounts for residents are available, a checkbox will show above the search button.
When you check in at the port, you'll need to show valid proof of residency. If you cannot provide this, the ferry company will ask you to pay the price difference for the non-discounted ticket.
All passengers on the booking need residency for the discount to apply. If one or more of your passengers does not have residency, you'll need to make two separate bookings to get the best price.