The short answer between the Marine Corps and the Army is one of training.During wartime the U.S. Army may draft in order to raise the numbers it needs.
The USMC does not draft.
USMC training is more than twice as long as Army training.
In essence the marines are meant to be a more "elite" force with its roots in being naval infantry to seize and capture coastal areas in support of larger army and naval operations. The marine corps was called on to do much more than this especially in World War II as most of the Army was concentrated in Europe.
In essence the Marines have evolved into a more "elite" army designed for rapid deployment and mobility. The marine corps is also unique in that it is the only branch of the military that has all combat resources it needs under its own command. (maine infantry, marine aviation, marine ships, etc)
For better explanation think of this scenario.
A major operation is being launched against a country with similar combat capability. (Let's say Russia, but this is only an example guys don't jump on me)
The order of battle on land would be for US Marines to perform any initial landing to capture ports or other landing zones. From there the Marines would proceed inward in the initial thrust supported likely by Army units trained in cold-weather environments. US army units would advance on the flanks and capture secondary targets.
Marines are meant primarily as an offensive force designed for rapid mobility. This is why the marines have had a bit more trouble in Iraq than the Army has the Marines were not built, trained, and equipped for this type of mission. Marine involvement has been mostly to supplement Army forces which have more training in that type of duty.
I may be rambling a bit and the truth is in recent years the line between the two services has been blurred. If the question is still open think of the Army as "Regulars" and the Marines as "Shock Troops" for comparison between the two.