One of the problems with the common representation of the War for Independence is that it tends to conflate several disparate military trends as unified, or subject to some sort of centralized, controlling strategy.
The reality was that the War for Independence was fought in several theaters with several different strategic goals and tactical doctrines that sometimes overlapped, or were sometimes used on concert or cooperation, and sometimes weren't. Victories in the northern colonies were often supported by guerilla activities hundreds of miles to the south, because they were able to split British attention, and the regular operations of the Continental army likewise allowed irregular, short-term, or ad-hoc forces to wage guerilla style warfare against areas in which British forces were less powerful.
Before we go on, let's set some terms. There were in essence two main divisions of land forces in the 18th century; the regulars and the embodied militia.
Regulars and Militia
Regulars were soldiers, who were contracted for a certain very specific term of service, paid wages, issued uniform, clothing, weapons, and food. They were utterly subject to military laws and military discipline which included quite harsh penalties for insubordination and desertion. They were expected and (when possible) trained to fight in the regular manner: firing ordered volleys from dressed lines, and using maneuver and discipline to multiply their effectiveness on the battlefield. This is often what people mean when they talk of "European" style tactics, but what you should know before we go on is that they were, contrary to popular belief, quite effective. They were also far more flexible than is often portrayed, as regulars could be employed as skirmishers, raiders, sharpshooters, and assault troops as occasion demanded.
Regulars were often split into different battalions of specialized troops, most especially, grenadiers and light infantry. These were often called "flank companies," because, at least on paper, each regiment would have a company of grenadiers and a company of light bobs, and would often be emplaced on the flanks of the regular line. In practice, when armies were formed, individual companies of regiments were detached into battalions or brigades of like troops. So rather than using the regiment on the battlefield, armies would employ battalions of regulars, battalions of grenadiers, or battalions of light infantry, pulled from the regiments at hand.
The job, on paper, of grenadiers were to assault fortifications or enemy lines. They retained their name from earlier doctrines in which they were equipped with grenadoes, but by the 1770s the use of grenadoes was extremely rare. Grenadiers, however, tended to be taller men with tall bearskin hats or mitres that added to their height. Their uniforms also tended to have slight visual alterations, such as more complex "wings" on the shoulders, to emphasize their size. They also retained their match-case, a small brass tube that kept coiled matchcord that was, in the days of hurled grenadoes, used to light the quick match on the grenado before throwing. By the 1770s it was an aesthetic thing more than anything else.
Then there was the embodied militia, which were "the body of the people in arms." The militia was the armed, organized expression of peacetime towns and cities, made up of men of "interest" in their communities. These men were civilians first, and soldiers second. The term "citizen soldier" is often used, and though somewhat axiomatic it it accurate to how militia behaved both in and out of battle. Though militia service was often compulsory, many men took great pride in their service, and in some places competition to be the (elected) officers of a militia regiment was quite fierce. Militia men supplied their own arms and their own uniforms, elected their own officers, and organized democratically, up to and including how they opted to coordinate with higher authorities. This meant that unlike the regulars, the militia had an expectation of consultation and cooperation with the military, and there could be tension between the military and civilians in strategic, tactical, and political senses.
Although this seems like a hideously incompetent system, it had grounds in political beliefs of the late 18th century as well as military necessities. British and American political systems were deeply suspicious of military authority, because any man or institution that expects and demands instant obedience might carry that tyranny into civilian life. Furthermore, even regular soldiers and officers were not expected to be career soldiers, but to temporarily serve in times of need and to retire back to civilian life afterward. The regular forces were so small and scattered that their training was itself rather superficial; regular soldiers would certainly drill more than militias, but often only in company or small battalion sizes, and depending on the time and place, certain militias might actually have more combat experience, man to man, than regular forces. In that sense, a massive crisis like the War for independence that suddenly had call for thousands of men to coordinate in extremely complex ways, was just as difficult for regulars to adjust to as it was for militias. Everyone was on the back foot in a major war, and the differences in "training" between regulars and militia is somewhat spurious. Even the efficacy and experience of regular officers was not guaranteed to be particularly qualitative; very few regular officers in the regulars had a great deal of combat experience, and the only difference in many cases was, again, that regulars had recourse to a system of military justice that demanded strict obedience. Militias, on the other hand, had legal mechanisms for refusal of service and negotiated leadership. It was much, much easier to hang an insubordinate regular than it was to do the same to a militiaman. A lot of the tension between these legalistic mechanisms has been morphed into beliefs about inefficiency or ineptitude, and that legacy is, more often than not, the one we have today.
Combat in the War for Independence
Despite the legacy of mistrust and inefficiency of the militia - Washington famously remarked that "placing any dependence on the militia is like resting on a broken staff" - the myths of American tactical superiority in the War for Independence are rooted in beliefs about the irregular warfare waged by minutemen and other voluntary, short-term embodiments of militia. However, many of the most successful engagements between the rebels and the British forces were spearheaded by Continental regulars fighting in the organized, linear methods of European armies. The Siege of Yorktown was in every sense of the word doctrinal, in that it relied on playing the playbook straight: digging parallel trenches, repelling sallies and destroying or capturing foraging parties. The siege was ended by a combination of French and American regulars making a nighttime assault on British redoubts to anchor their second line of parallel trenches.
Of course, the success at Yorktown owes quite a lot to the months of irregular, manpower and resource-draining guerilla combat in the southern theater of the war. This war was fought by militias and temporary musterings of volunteers who fought when opportunities presented and disbanded when they could. They helped to starve British garrisons of supplies and put British forces in a disadvantage when they had to concentrate to fight against Continental or French regulars.
Of course, the reverse was also sometimes true. The disastrous attempt of the Continental army to capture Quebec was composed almost entirely of American regulars against a patchwork force of British and Quebecois militia supplemented by a small garrison of British regulars, and the logistically nightmarish march through the wilderness of Maine had so sapped the American force that it was at a fraction of its potential power during the decisive battle.
I would also like to point out that on both sides, participation of local potential forces - militia and volunteers who were not embodied but could be - was sometimes dependent on the success or perceived success of the regular forces nearby. Following the success at Bennington, for instance, local militia swelled rebel ranks up to the battle of Saratoga, and the swarms of volunteers and irregular forces not only bolstered manpower but stretched the British ability to deal with them, further giving rebel forces an advantage.
So, in answer to your question - did they "switch" styles? Yes, but not really in the way you've phrased it. Regular and irregular forces worked in parallel throughout the conflict, and successes of one helped to support the actions of the other. Furthermore, European military doctrine was flexible and creative, and made extensive use of irregular detachments and skirmish forces. Militias, too, sometimes fought in concentrated, dressed lines and exchanged volleys with British regulars and loyalist militias, and also employed irregular tactics for raids and sabotage efforts. But the nature of the force compositions meant that it was much easier for a temporary militia muster to embody for a temporary emergency and disband afterward; something regular forces couldn't do by the nature of their organization and legal standing.
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