From the official Ft. Benning website:

-The 75th Ranger Regiment is a Special Operations unit with the mission to plan and conduct joint special military operations in support of U.S. policies and objectives. The Regiment is the largest Special Operations direct action force.

-Ranger School is the Army’s premier leadership school and falls under the Ranger Training Brigade (RTB) at Fort Benning and the Maneuver Center of Excellence (MCoE).

-The 75th Ranger Regiment does require that its leaders attend the U.S. Army Ranger School; however, it is not a pre-requisite to join the Ranger Regiment in all instances. All Infantry and Artillery Military Occupational Specialties (MOS) must complete the course before they assume a leadership role in the Regiment. The remainder of the MOS’s in the Regiment send their leaders when they are ready.

Got that?  The Ranger Regiment is a Special Operations strike force, Ranger School is a training course that teaches tactics and infantry leadership skills.  Don’t screw this up!

Let me also add a few notes of clarification:

When NCO’s in the 75th Ranger Regiment have to do their instructor time, some of them end up becoming instructors at Ranger School so there is some cross-over from the 75th to RTB.

In regards to the Best Ranger competition that is held annually, anyone who has graduated from Ranger School is free to compete, not just members of the 75th.