Waiter serves you, assistant waiter serves waiter. No seriously, the assistant waiter is really in almost a team position with the waiter. He is more like a bus boy, in that he will fill your water glass and bring the bread, clear your plates and serve the coffee. The waiter takes your order, brings your food, often serves the wine,and is generally responsible for the table. In a good team this works out perfectly, remember the waiter has many other talbes to do ( not just yours) and so the team approach should cover all the service needs of your dining experience.
Pg is correct, they both work together, they each do their own jobs to make your dining expierence the best. In almost all my cruises, having dinner in the dining room is something to look forward to and hopefully you'll get tablemates that you enjoy eating with.