I would like to thank /u/TRB1783 for the shout out and the information he gave. Rather than reiterate what he said, I would like to,build upon it and add a few comments on other things you said.

First to just clarify something. Linear Tactics =/= Napoleonic tactics. Linear Tactics refer to a system of military combat where an army revolves around the linear aspect of the line, creating one long, unbroken line which the enemy mirrors. The linear aspect refers to the uncreative and simple tactics involved which rarely involve maneuver.

The Napoleonic Era (which can be shouldn't be used as a blanket term for the Revolutionary and Napoleonic era) does see soldiers fighting in lines but only after movement. Further the Napoleonic era shows a return to decisive combat where armies would clash in a big, climatic battle which would determine the fate of their nations.

So, Napoleonic warfare is much different than linear or (in the broader sense) dynastic warfare. Dynastic warfare, the type of socio-political means of solving problems of the state through warfare as war and the state are tied together most during this time period. Warfare is waged for Kings, not the people. As such, the state raises and maintains armies, which often were pulled from commoners with a sense of adventure or the dregs of society. With these men being raised by the state and effectively held there through the use of extreme measures, men were shipped (sometimes literally) into an almost mechanical being that marched, reloaded, and fired with extreme precision. This was able to be achieved through use of force, coercison, and the fact that armies rarely were larger than sixty thousand men (as armies were funded by the State, it is a burden and thus wouldn't be overly large).

With the French Revolution, corporal punishment was largely pushed out of the French army, allowing men to have a bit more relaxation and with the rise of large armies, there was little to no point in training men to be mechanical beings. Now they fought for France and their families, the purpose of war changed from being a tool of Monarchs to that of self defense and liberation.

Finally, the thought changed. As I mentioned, soldiers were trained to be mechanical, precise. Military science and theory at the time saw warfare as something that could be quantified and qualified, something that could benefit from the Enlightenment ideology of order. As such, soldiers were pushed to be a machine to reign in the excessive destruction of the 30 Years War. However this would fall out with Revolution, with mass conscription there would be little precision, yet far more elan.

As such, this doesn't mean that it was all gone by 1815. The enemies of Napoleon used it until they were utterly defeated, and as the British were never properly defeated by Napoleon, they still used fire by rank up into 1815.

I think /u/DonaldFDraper can speak to the shako-wearing period a bit better than I can, but by the mid-18th century, armies employing linear tactics (the solution to your desire for a general name for this kind of warfare, btw) often preferred to keep up a steady stream of fire rather than fewer, larger volleys. This was usually satisfied by firing by platoon. This made sure the enemy was always receiving fire, and was thus constantly pressured. It also kept enough of the regiment with their muskets ready to repel a sudden charge.

By the time we get to the Napoleonic wars, the French have adopted a volley-by-files, where each two-man (front and rear) component of the line fires at a time, working from one end of the line to the other. The result was intimidating for people on the receiving end, as a soldier could see the wave of bullets scything towards him.

Sources: Von Steuben's Blue Book

Matthew Spring, With Zeal and With Bayonets Only

Russell Weigley, The Age of Battles