To help clarify some terms used:
Pax=passengers
Metal=plane
Carrier=airline
Ticket stock=refers to which airline issued the ticket. Their 3-digit number will appear at the beginning of the ticket number. This can be different from the. . .
operating airline=the airline flying the flight. This usually means that it's their crew and metal. This is the airline you would need to check in with when arriving at the airport.

Hope that helps!