A CRS/GDS locator (PNR, the 6-digit alphanumeric code often used to identify tickets, but really only points to a GDSs database entry) and a ticket are not the same thing, though. A PNR can include non-air travel segments like hotels and rental cars too, for example.

That's something very different from a single airline issuing a ticket for a complete itinerary, which importantly makes them responsible for getting you to your final destination in case of missed connections, checking your baggage through etc.

If you still have the confirmations or boarding passes, you could check for the three-digit numeric e-ticket number prefix, which defines which carrier actually issued the ticket.