I would guess its a offshoot of starfleet security but focused on offensive rather defensive warfare in larger units rather than piece meal away teams.
I would also see them being homogeneous i species to take advantage of there diffrent traits IE A vulcan hot weather regiment or Andorian Cold weather temperature.
My current 'allocations' for the original Founding members is:
Starfleet Security (or Starfleet Tactical) Special Operations Service:
1st Spec Ops Group (Diplomatic/Executive Protection) - Earth^.
2nd Spec Ops Group (Cultural Assessment, Recon & Evaluation) - Vulcan*
3rd Spec Ops Group (Special Hazards and Rescue Command):
>> 1 Corp (Polar/Maritime Rescue) - Andor
>> 2 Corp (Desert/Mountain Rescue) - Tellar
>> 3 Corp (Space Rescue) - Alpha Centauri
^ - primarily acts as tactical support to the FSA, also acts as overall Type Commander for deployed and static SpecOps units outside the original five.
* - supports tactical and security objectives within medium to long-term "First Contact" missions. During declared state of war, integrates with the Starfleet Intelligence Rangers in the 'force recon' role.
Completely non-canon of course, but I think it fits reasonably well into what Starfleet
should have.