Originally spetsnaz was applied to the DOD special mission units. But everyone needs a legend and some wanna be that legend. SpN units are not rubber, they can't accommodate everybody who wish joining. The attrition is high even now when it's not so popular among youngsters. When I knew more on the problem it was only 6,7-8% PASS for the initial training for the naval part of the community and a bit higher for the army part... So those who FAIL go other places and make them fancy by legends and fashionable words. Spetsnaz is a very fashionable word here...To be fair, in post Soviet countries, even riot police is often publicaly referred to as special unit / spetsnaz.
And it is. The idea is we have a bit another approach to the special operations. We have different agencies that have different tasks. Alpha belongs to FSB and is tasked of getting terrorists, sabouters and intelligence agents mostly friendly territories or as you would have said, in the US CONUS and OCONUS. FSB has some more SF that are also SMUs, but for another mission.I thought Russian smu was Alpha group.