Check out Cornell's U.S. Code:
TITLE 10 > Subtitle A > PART I > CHAPTER 13 > Sec. 311. Next
Sec. 311. - Militia: composition and classes
(a)
The militia of the United States consists of all able-bodied males at least 17 years of age and, except as provided in section 313 of title 32, under 45 years of age who are, or who have made a declaration of intention to become, citizens of the United States and of female citizens of the United States who are members of the National Guard.
(b)
The classes of the militia are -
(1)
the organized militia, which consists of the National Guard and the Naval Militia; and
(2)
the unorganized militia, which consists of the members of the militia who are not members of the National Guard or the Naval Militia
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Thus, per Section 1, the "Organized Militia" includes the NG. It is part of the Militia, just not part of the "Unorganized" Militia.
Regarding the Minutemen, my understanding is that they were both better trained and ready to get to battle a lot faster than the average member of the militia. I would agree that the vast majority of the militia was badly disciplined and badly (if at all) trained, but I don't think that this applied to the Minutemen. What, after all, would be the point of getting a bunch of undisciplined, badly trained people to a battle quickly - so that they can be killed first?
Large volumes of fire. Muskets weren't aimed; rather, pointed.
TITLE 10 > Subtitle A > PART I > CHAPTER 13 > Sec. 311. describes the federal militia, not the well regulated state militia to which the second amendment refers.
Ah, you are correct about "unorganized" vs "organized" - the NG is PART of the latter. However, look at your organized again for the main point. The NG is not THE militia all in itself, in any class.
ALL males of the correct age belong to the militia! Whether you are aware or not, YOU belong to a militia! ;-)
Back to the minutemen (not capitalized, BTW) - no, there was nothing particularly special about them. Only that they were to be "ready in a minute" - to leave!
These men did not have anything special beyond what a "regular" militiaman had. They simply were expected to show up rite away on a moment's notice. There were no regimentals, no special muskets, nothing. Indistinguishable from other militia as far as field discipline.
And your last comment belies the point of minutemen - they were not expected to go to real battles, per se. They were essentially "alarm" contingents for emergencies. They wouldn't follow main armies around to fight for them. They were meant to "stem the tide" until perhaps more men - or better (ha ha, that's another story) - could get to the scene. The Concord action, e.g., was hardly a "major battle" in terms of the enemy. It was only like a regiment or so. But the main point is, these were guys who were "on call" and aware of it, just for emergency situations.