This has me wondering what the major differences are between Rangers and Green Berets. I'm thinking that the Green Berets are the elite forces from the Rangers. Is this correct?
For a quick and dirty cut/paste answer (that is mostly accurate)
"Green Berets" are Non-commisioned officers that have passed the Special Forces Assessment and Selection program and reclassified into an 18-series MOS upon completion of the Special Forces Qualification Course. they are generally assigned to one of the 5 active duty groups upon completion of training. There are also currently 2 Special Forces Groups in the National Guard force structure.
"Army Rangers" are members of the army assigned to the 75th Ranger Regiment either in headquarters or in one of the three Ranger BNs. Members of this unit go through a Ranger Indoctrination Program before being assigned, and if found lacking motivation or ability, they are released back to the needs of the army. Not all members of the unit are "Ranger qualified"--meaning that they have not successfully completed Ranger School...but this is generally understood to be a requirement for promotion to Sergeant in the Regiment.
Many "Green Berets" are "Ranger Qualified" or "Ranger tabbed" but the focus and mission profile of Special Forces Groups and the 75th Ranger Regiment differ in rather extreme ways.