The MMC and TWIC Cards are needed only for US Flag ships. FYI - it can take a very, very long time (3 - 12 months) to get the MMC Card. Until you have the card in your hand, you are not allowed to work aboard a US Flag ship. Aside from a few small coastal cruisers on the US East and West Coast, the only US Flag cruise ship is Pride of America in Hawaii.
For the other 350 or so cruise ships around the world, you will need a valid passport - not a passport card - to work there. You also need to pass a Level 5 Drug Screen - the same test that airline pilots take.