Combined arms military actions (or combined arms warfare) are, most generally, operations that involve the coordinated actions of different branches of types of ground troops (e.g., infantry, tanks, artillery). Joint warfare, in contrast, involves the coordinated actions of services other than the ground arm, such as navy, air force (other than air elements under direct army control) and special operations. Coalition warfare goes a step farther, in involving different arms of different countries, under a common command.
In the Second World War, the British term was "combined operations". German blitzkrieg worked at two levels: the high-speed breakthrough by coordinated tanks, motorized infantry, artillery, and close air support; followed by securing the flanks by conventional infantry. These German and British techniques were not fully joint, in that the strategic air forces operated independently, and indeed, the U.S. and British strategic bombing generals might complain bitterly if they were asked to carry out a mission for another service, such as the mining of Japanese waters or using heavy bombers in close support of an invasion or breakout.
Combined arms and doctrine has been a specialty of the United States Marine Corps. Its current Marine Air-Ground Task Force structure arguably is more of joint than combined arms structure, as it tightly integrates high-performance aircraft to the needs of the ground commander, usually as a substitute for the artillery of heavier land forces. Naval infantry like the Marines, however, normally are on the border between combined and joint, since they rely on a navy to deliver them for amphibious warfare, usually providing them with naval gunfire support and sometimes additional close air support from aircraft carriers.
Traditionally, a staff that dealt with multiple types of ground troops had "G" prefixes for its sections, while a staff that dealt with multiservice operations had "J" for "joint" branches. While the term has been used to describe multinational operations, those are more commonly called "coalition" operations; a staff integrating multiple countries has "C" sections.