Legacy Airlines: Officially those which conducted inter-state flying prior to de-regulation in 1978. Only five left: AA, DL, UA, AS, HA

Colloquially speaking, people often mean "Big Three" when they use the word legacy: AA, DL, UA.

Major: Any 121 airline which sells pax tickets under it's own brand, and has that brand painted on it's aircraft.

Majors are often categorized informally in "tiers", which generally reflects the size of the airline, as well it's desireability from a pilot career perspective:

Tier 1: Typically Big Three, FDX/UPS
Tier 2: Typically AS, B6, HA, maybe NK, F9, Allegiant
Tier 3: Small niche pax airlines, startups, most frieght, charter, ACMI, random cats and dogs.

Regionals are not majors, they don't have their own band, but some might be better careers than some tier 3 majors (mostly due to job stability).

SWA could be either tier 1 or 2, depending on your perspective. They just got a good contract, but they don't have the kind of retirements as the big three so from a career perspective most folks are better off at big three, with most other factors equal.