Air Force Reserve units tend to reside at Active Duty bases while ANG units have their own bases. I can only speak on the ANG w/ certainty as I've been in for about 5 years now (C-130 unit).
The ANG does fall under the DOD and serves both the US Government and the State of AL, AK, DE, WV, VA ... etc at the same time.
The common misconception is that ANG units stay in the US and are only responsible more or less for homeland security. ANG units are overseas with the Active Duty right now, were during the war, and will continue to do so.
If a recruiter tells you ... "one weekend a month, two weeks a year" he's blowing smoke up your butt because that is just not the case anymore.