The "major airline" criteria of $1B in annual revenues has nothing to do with flag, domestic, or supplemental ops. These ops are all defined in part 121, and a 121 airline may be certified for one or more.
Domestic: Exactly what it sounds like, except I am 99% certain that Canada and Mexico qualify as Domestic (vice Flag) for the purposes of part 121 classification. Warning: Canada & Mexico are DEFINATELY international destinations as far as passports, radio licenses, ICAO rules, and all that other stuff.
Flag: International flying over lots of water.
Supplemental: As was mentioned, a 121 airline certified for supplemental ops may perform unscheduled charter-like flying, but the operating rules are different than for domestic or flag. They are also different from 135.
My experience is that most US airlines are certified for at least domestic (obviously) and supplemental ops (to support military charters if nothing else). This includes regionals of any real size. The big legacy carriers are obviously flag carriers also.
Last edited by rickair7777; 12-18-2006 at 08:30 PM.