Codeshare
I stupidly once thought that if I bought a ticket from United, the same airline would be flying the plane. And this thought — plus, stubbornly insisting that I was right — caused a lot of embarassment when I later realized my mistake.
Codeshare, that's what they call this airline switching thingamajig that they do to mutually help each other out.
Codeshare, as defined by Wikipedia, "refers to a practice where a flight operated by an airline is jointly marketed as a flight for one or more other airlines. Most if not all major airlines nowadays have code sharing partnerships with other airlines, and code sharing is a key feature of the major airline alliances."
Learn the whys and wherefores of codesharing by heading on out to this page to avoid confusion or, horror of horrors, miss your flight.