Tankertrashnav
Yes, there very much are definitions as to what special forces are.
The British use Tier 1 and Tier 2 classifications. The SAS (regulars) and SBS (regulars) are tier 1. SAS, SAS signals and SBS reserves are tier 2 from memory. The SRS are tier 2 I think. The Royal marines, Paras and RAF regiment are not special forces. With regards to those three although 2 sqn RAF regiment have a good reputation its training regime and five miler of death fall way short of the other two units...............A five mile run just isn't in the same league as the thirty miler a commando would do!
While the pathfnders are 'ordinary forces' some people would consider them as tier 2 level. The same applies to soldiers who are patrols qualified*
Going back to SFSG, while it comes under the director special forces, only soldiers in the unit could be considered as tier 2 soldiers, soldiers in normal RM, Para or rockape units are very much ordinary forces.
*The British army has three arduous training courses:
Special forces selection
P company
Patrols course (it has a newer name, but is often called patrols course)