The NG is the last remnants of the militia. They are still under the
purview of the states tho, hence the state name in front of each
unit's name. You are right, that is not the same as the reserves which
are directly connected to each service.
The Coast Guard has always been a different breed of cat. It is and
has been a civilian service that can be called up by DoD. They still
follow all of the military customs, UCMJ etc but they have always
worked for some other civilian agency, not DoD. They make that pretty
clear to you when you are there. I was there for the Treasury days and
the Transportation days. DHS happened after 9-11.
They are really a strange hybrid with pretty much unequaled powers.
They have the power to enforce laws without bumping into Posse
Comitatus, they can enforce immigration law, they can board and search
vessels at sea without a warrant and that extends into just about
anywhere they have jurisdiction. You see that in action here when they
will put some junior enlisted coastie on the sheriff's boat during
those enhanced enforcement weekends so they do not have to deal with
niceties if they want to look over your boat. They just send the CG
guy on board to look around. The CG does have the power to
immediately seize your boat if there are drugs on board, in any
quantity. I often wonder if that has ever been tested in court if they
are inside the COLREGS line. I know offshore guides are pretty adamant
with a "no drugs on my boat" rule.
The Coast Guard can also operate under the Navy's jurisdiction and
control in certain circumstances.