Technically getting back on board only requires the ship card. Actually getting to the ship, through the port, is where the need for photo id comes in.
Some ports are really strict and some are not even with the US ports. One of my stops on my last Alaska port you had to have photo id the other 2 no one ever asked the ships card was all you need.
Bottom line take photo id if you are 16 or over - you may not need it but it will be bad if you do and don't have it.