Majors actually contain a couple of sub-sections: National and Legacy. Traditionally Legacy airlines have established international routes but the lines have gotten somewhat blurry. I fly for Hawaiian which is definitely a Major but some consider it a National and others a Legacy but ultimately it really doesn’t matter. Now Delta, United and American are all legacy carriers, but airlines like SouthWest, Atlas, JetBlue, etc all fall under the category of Major. The main difference between most Regional carriers and the Majors is the Majors sell their own tickets and the Regionals do not. The Regionals support the Majors primarily by bringing passengers to their hubs. A person may by a ticket from say Boise to LAX on United but they’ll actually be flying on SkyWest on a smaller plane painted with United colors. The Regionals generally fly smaller aircraft and offer lower salaries. Those are the basics.