No, you are confusing Special Operations units with names of their own, with Special Forces, which is the official name of one of those Special Operations units.
I can’t understand how you can’t learn the name of the Green Berets, did you think they were really named a hat?
Do you think when a Special Forces soldier and an Airborne Ranger soldier meet, the Ranger says Special Forces? me to!
The U.S. Army’s 1st Special Forces Operational Detachment-Delta, popularly known as Delta Force, is the first of the two counter-terrorism, special mission units that fall under the Joint Special Operations Command
Note that Delta Force has Special Forces in its name.