Is the National Guard the "militia?"
A bit of research into the legal background of the National Guard can be revealing.
There is of course the modern 10 US Code §311, which defines the unorganized militia of the U.S. as essentially all males 18-45 and certain women, and the organized militia as essentially the National Guard. There are also various State statutes (Arizona's defines the state militia to include women as well as men).
10 U.S.C. §311 dates from the Dick Act of 1903, which repealed the Militia Law of 1792, and first wrote the term "National Guard" into law. The Guard as we now know it (dual enlistment: members of State National Guard units required to enlist in the U.S. Reserves) dates from the Army Act of 1940. (Why dual enlistment? In 1912 the Attorney General ruled that NG units could not be sent outside the US, because they were part of (note "part of") the militia, and the Constitution allows the militia to be called up only for domestic purposes -- to repel invasion, suppress insurrection, and execute the laws of the Union. As a result in WWI Guard units were broken up and members drafted into regular Army units as individuals, an inefficient operation and one displeasing to the Guard).
So let's take a look at the legislative history of those statutes....
Debates over the 1903 Dick Act: Original proposal was to have National Guard and also two classes of volunteer reserves, consisting of NG units that had volunteered as federal reserves and whose officers would be approved in advance by the Army, and who would be available for service overseas (that is, the Guard itself would be more like the modern State National Guards, and the volunteer reserves would be more like the modern National Guard).
House debates (35 Cong. Rec., (1902)
Rep. Wiley (p.7111) "In my remarks on this occasion it is not my purpose to discuss the militia in its widest sense, as including the whole military force of the nation. I shall confine myself to the great body of the citizens in the different states and territories of the Union who, actuated by patriotic impulses, have enrolled for instruction and discipline as a reserve force ..."
Rep. Stark (Appendix p. 387): "To my mind our institutions are best served by having a small regular army as nucleus, garrison duty, and the first line of defense; then for the support to be first called out, the organized militias commonly known as the "National Guard;" then for the third line, the national volunteer reserve ... Then comes the reserve militia, which includes all able-bodied men between the ages of 18 and 45."
Sen. Proctor (36 Cong. Rec. 125 (Dec. 9 1902): "The old law makes every able-bodied man in the country a member of the militia, and provides no further organization. This bill separates and makes a class which can be called into active service."
Proctor, at p. 305: "The National Guard is in full organization; it is already created and would naturally be first called upon if wanted for a limited time, and then the militia would be called upon."
At p. 299-300, Sen. Pettus objects that creating the volunteer reserves might exceed Congressional powers over the militia, since their officers are approved by federal authorities and the States have no control over use of these units. [The Constitution provides that the States shall appoint officers of the militia] Sen. Proctor responds "The troops provided for in section 24 are not militia. They are volunteers. They are called the national volunteer reserve, as the Senator will see. They are not called militia."
At p. 303, Sen. Foraker backs Proctor: "[W]hile this reserve is part of the militia, in the sense that all men are a part of the militia who are between the ages of 18 and 45, it is not a part of the militia in any other sense.."
P. 354, Sen. Bacon, in opposition, says that if this volunteer force were the militia, it would clearly violate the letter of the Constitution. He continues, "There is no possible question about the fact that it is not part of the militia, so far as the letter goes. But I think it is violative of the spirit and intent of the Constitution in that it makes a part of the regular establishment that which the Constitution intended should be the militia."
Debates on the 1940 Army Act (86 Cong. Record, Aug. 1940)
Sen. Gillette: (p. 9914) "The militia of the United States are citizens between certain ages capable of performing military service. That is the militia of the United States. It consists of all citizens of that type, and is divided into the unorganized militia, the organized militia, and certain naval units. The National Guard of the States and Territories are organizations composed of these militiamen, members of the unorganized militia, who voluntarily have enlisted in specific organizations for a specific purpose with a specific limitation. That is the National Guard of the Nation. There is a third category, the National Guard of the United States. That organization is set up under a specific act of the Congress ..."
Sen. Sheppard (p. 9985) cites a 1916 statute parallelling 10 USC 311, and also defining the army of the US as the regular army, the National Guard, etc. He explains, "Every National Guard man who takes the oath takes it with the understanding that he is part of the Regular Army ...."