Okay, DNS, I'll bite. The "National Guard" actually refers to 50 (or more? do territories have their own?) different organizations, such as the California National Guard, the Kansas National Guard, the Montana National Guard, etc. When I enlist in the Montana National Guard, I actually say a different oath than a federal soldier does, in that I swear loyalty to my state as well as the nation.
The reason it's the California National Guard, instead of the California State Guard, is because by having a state military presence across the nation, we actually help defend the nation.
The point of the various National Guards, in theory, is to provide a first-line defense of the country in case the regular Army is tied up, and to provide rapid on-scene responses for emergencies. It is (or was) not intended to be used as a federal force. If the federal government wants a state's troops, they have to ask. They can cut federal funding if the state says no, which makes it unlikely when push comes to shove that any state would do so, but the point is that the governor can.