The difference between a Second Officer and a First Officier depends on the airline. In some airlines the Second Officer is a cruise pilot, ie thye sit in the seat for the cruise part of the flight whilst the First Officer and Captain take turns at having a rest. The First Officer and Captain sit in the seats for take off and landing.
In other airline a First Officer and Second Officer are basicaly dependent on experience , often the pilot is a Second Officer until they complete 1500 hours and hold a full ATPL.
The Captain does exactly the same job but carries the buck at the end of the day for any mishaps. The Captain will have the final say in any decisions made, USUALY in consultation with the FO. He/She has the responsibility for the safety of the aircraft and all those on board it.
In most airline the SO, FO and Captain all fly the aircraft. The old adage that an FO doesn't fly is rubbish.