I don't know how this plays in DC, because DC is weird. But generally, Guardsmen operate under two separate authorities of US Code: Title 10 and Title 32. Title 10 is the same as active duty, and involves the Guard being federalized. Title 32 is the framework under which Governors can call up their individual state militias for active duty within their states. The Guard can have some law enforcement authorities under Title 32, but this isn't allowed under Title 10 because of Posse Comitatus. I'm not clear on what the boundaries of that are. There is also
Title 10 §12406, which partly deals with hostile military invasions of CONUS, but also allows the Guard to be federalized when "there is a rebellion or danger of a rebellion against the authority of the Government of the United States," or "the President is unable with the regular forces to execute the laws of the United States."
Pretty sure 10 USC § 12406(2) is the modern equivalent of Lincoln calling up the militia in 1860, and 10 USC § 12406(3) is more an LA Riots-level thing. No idea how the Insurrection Act plays into all of those MOB authorities. But the Guard is distinct from the Reserves legally by being the organized militia of the individual states, not a Federal formation.