US Military Term
Originally this term was the designation for Vietnam-era Special Forces Groups, called "SOGs". MACV-SOG, or Studies and Observation Group, was a cover-name for Special Operations Groups. These units were the elite Special Forces Groups operating in that era. The term was changed after Vietnam.
This term usually encapsulates all Special Operations Forces, or more specifically, a Special Forces Group when applied to the Army, although the term is not technically correct. This term more or less refers to all of the elite forces that compose America's most trusted and highly trained units.
Special Operations Forces
As stated above, the term Special Operations Group usually means Special Forces Group in today's sense, when applied to the Army. But when used in a general sense, it applies to all SOF forces. As Roninspoon pointed out, it isn't the actual name of any command or department today.
Roninspoon says re Special Operations Group : SOG is a gernarlized term, not an actual department or command. After Vietnam the MACV-SOG were reorganized as Special Operations Forces until shortly after the Iran Hostage failure at Desert One. Several years of congressional review followed an in the late 80s the SOF was reorginized as USSOCOM, a joint task force command of SO operators. http://www.socom.mil/ has plenty of info including a huge PDF doc detailing the command's history.
Noung says re Special Operations Group: Nice one, but what do you mean by "today's sensitive civilian battlefield" exactly? Can you expand it a bit, what do they actually do? - Civil affairs works to win the hearts and minds of the Iraqis, and any peoples that live in an area we operate in, as does PsyOps. They are the unsung heroes out there building schools, working with local officials to provide power and water, talking to the Iraqis about their opinions, giving out food and water, and all the things the doomsday media doesn't report.