There are other Special Forces than the Green Berets. You are missing the trees for the forest with your pedantism.
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!