Mr. Mephisto,
The US military has three main branches: the Army, Navy and Air Force.
The Marine Corps is officially part of the US Navy. They were originally the on-ship troops back when ships fought hand-to-hand, now they are designed as the main seaborne invasion force, though they are used everywhere. Their training is longer and more difficult then any other branch, so they are a different kind of soldier.
Most of the rest of what you listed is under the Army. The Green Berets and Rangers are special-forces units, for dangerous missions. The 101st Airborne is designed as the paratrooper division.
The SEALS are part of the Navy, but are their version of special-forces.
I hope this helps, and I REALLY hope it's all right, as it comes from my memory
