Getting back to the original question, I can answer best by describing the various units around my home town in central Missouri.
We have a large community of German immigrant families all along the Missouri River. This group was well established by the time of the war but still seen as outsiders by many people. The Home Guard unit in my town was commanded by Capt. (later Col.) Joseph Eppstein, and consisted primarily of Germans. One exception was Walter Barron, an Irish immigrant. This unit was well drilled, apparently well supplied and was garrisoned in an earthen fort that has been discussed in other threads here. They did, indeed, fight a significant battle against a numerically superior force of Missouri State Guard cavalry, and they repulsed the attack on their fort. Eppstein had operated somewhat beyond the law by arresting several prominent southern-leaning business leaders and keeping them as hostages inside his fort. Using them as leverage (and one of the hostages as a spokesman), he was able to negotiate the withdrawal of the State Guard to three miles outside of town! Later in the war, Eppstein's unit did serve with militia and perhaps regular forces elsewhere in the state. Our town had various companies of regular occupying troops by then.
A second unit that we've discussed here several times was the Missouri State Militia garrisoned in Fayette, Missouri and commanded by Major Reeves Leonard. This was a federally sanctioned, supplied and paid force that was well trained and disciplined. They were engaged in numerous fights with guerrillas and occasionally against regular forces. Another excellent company of MSM was garrisoned in Columbia, Missouri and commanded by Col (later General) Odon Guitar. (Yes, that's his real name.) One interesting condition placed on the formation of the Missouri State Militia is that they could not be forced to operate out of state. They were seen as a federally sanctioned and supported defense force within the state. Some MSM units did serve occasionally outside the borders of Missouri, but this would have been voluntary service. Presumably, with the agreement of the Governor and the legislature.
A third type of unit that became sort of a plague on the state was variously known as the Enrolled Missouri Militia or the Missouri Enrolled Militia. This organization was formed under state law and service was compulsory. The various companies were often poorly led, poorly trained and poorly supplied. They were frequently corrupt and were little better than some of the worst bushwhackers. Some men who had returned from service in the Missouri State Guard (southern) and had taken their oath of allegiance did join the EMM, but not with the intention of actually fighting against their former comrades. Some units consisting almost entirely of former southern men were sympathetic to the Missouri guerrilla cause. They became known as the Paw Paw militia. When the opportunity arose, many deserted and went back into Confederate service. Other former State Guard men refused to join the EMM, and eventually joined a guerrilla band or left the state. The noted Quantrill man, John McCorckle, discussed the problem of the EMM and his decision to "go to the bush" in his memoir.
As I said, the answer to the original question is somewhat complicated. I can't speak for Home Guards or Militias in other states. I suspect they varied, too.