I realize that airlines can operate with different numbers of Pilots and Flight Attendants, depending on the route, aircraft and length of flight (EET). Which are the types of crew members that an airline can have, with the correct titles? I've heard about captains, master captains and cruise captains, but how can I identify them during the flights?
As the EET is variable from flight to flight you should better say that it is dependent on specific kinds of operation or routes, which is quite the same but includes also the time before and after the flight. Flight duty time starts at check in and ends at check out.
There are general requirements based on the maximum allowed duty time of a crew member, which are again based on the regulations of the aviation authority of the operators country. Finally it differs from airline to airline and is regulated by the operations manual, which can of course be not less restrictive than the authority, but there are some general titles you often hear:
Captain The Captain is the PIC (pilot in command) of this flight and responsible for a safe operation. He must be on station for departure and arrival.
First Officer The F/O is also found on every airliner operation. On short or medium ranges he is the 'Copilot', some airlines fly with two F/Os on long haul flights and in some portions of this flight most probably the two F/Os are in the cockpit and the captain takes a nap.
Second Officer When starting at an airline, you sometimes begin as a S/O and are only alloweed to do specific tasks. So for example handling the radios during departure and arrival, or having the controls during the cruise phase.
Cruise Captain Well, read the name ;) He might be a Captain and only in the function of a Cruise Captain for a specific flight, but once again, it depends on the operator.