In military parlance “regulars” refers to troops in an established, full-time force like a national army. “Irregulars” refers to part-time or on-call troops in a militia or temporary force.
“Regulars” are thought of as better trained and more experienced, but they have still been defeated by “irregulars” from time-to-time. These were generally state militia in the U.S.
During the American Revolution all the British troops were “regulars”, including the German mercenaries. The Colonials were all “irregulars” at first, until the Continental Army was formed.
With the establishment of a permanent U.S. army after the Civil War, and later the establishment of National Guard units in the states, the official militia system fell out of use. It was recognized as a danger to liberty because some state militia leaders advocated overthrowing the government.
Today, the term “militia” has been usurped by right-wing extremists in an attempt to justify gun ownership, political paranoia, and racism.