The first difference between the US army and its marines is size. The army is greater. Secondly, the army is land-based whereas action from the marines is amphibious and begins from their sea-base.
Thirdly, you can enrol with the army up to the age of 35. Its maximum enrolment age is 28 for the marines whose description is 'an elite fighting force' - hence the phrase or joke, 'leave it to the marines' suggesting only they can resolve really difficult situations.
There are many differences between the Army and the Marines. First, to join the Army, you have to be between 18 and 35 (although you can join with parental consent at age 17). To join the Marines you can be no older than 28. Basic training in the U.S. Army is 10 weeks long and for the Marine’s boot camp it is 13 weeks long.
These are minor differences of course. The big difference is that the Army is a much larger force and it is the oldest branch of the US military. The Marines are part of the Department of the Navy.