I was under the impression that the bayonet lost prominence over time, and specialty troops such as light infantry began to see more action. But other than that, I'm not very sure how one period differed from the other. There must have been some significant changes over the time of the Spanish Wars of Succession and what was the beginning of the Napoleonic Wars, even though in most media depictions, the warfare is portrayed as virtually identical.
How did the actual combat engagements change during this time period both technologically and tactically?
edit: Additional question. What would an engagement be like for an infantrymen/company in a standoff? How long until the other side broke and what factors went into victory?
I was under the impression that the bayonet lost prominence over time
Not really!
In reality, one of the big changes that came about at the end of the 18th century were the tactics of French Revolutionary armies, which often involved massive bayonet charges to overwhelm enemies with elan. Look at, for instance, the Battle of the Bridge of Arcole in 1796. A general of the earlier 18th century likely would not have risked such an assault on the fortified Austrians, but, since French infantry were relatively untrained and drafted in large numbers compared to the smaller, professional armies of the earlier 18th century, they could not be expected to trade volleys or manuever in a fashion to force the Austrians away, but they could all rush at the position in a headlong assault, which, surprisingly, often worked!
If you're curious about this, I would recommend reading two books together, or one after the other. Warfare in the Age of Marlborough and then the famous Campaigns of Napoleon by the same author.
Oh boy, this is actually a huge question due to the sheer number of conflicts in Europe during the 18th century, and to the fact that evolution came gradually to different countries. I'm sure that /u/vonadler will stop by to explain far better, but as an example the pike had been abolished by most western states (Britain, France, the German states) by 1700, while the Swedish Empire was still using mixed pike and musket when it lost its army against Peter the Great at the Battle of Poltava in 1709. Uniquely, the Swedish infantry were also equipped with rapiers, the only land army still fielding swords. Swedish tactics were built on disciplin and shock, built on marching on the enemy lines in formation and then unleashing one or two short range volleys before charging the enemy with rapier, bayonet or pike.
According to the historian Peter Englund these tactics had served the Swedes well during earlier 17th century wars and primarily at the Battle of Narva in 1700, where the Carolean troops soundly defeated the ill trained Russians, but by Poltava Peter had soundly reformed his army. While most of the blame can be attributed to Charles XII and his generals and their faults are too many to mention (though I'd love to), at Poltava the Swedes suddenly faced Russian infantry who wouldn't simply turn and run when they charged, denoting the end of the Swedish shock tactics.
On the other hand, the Russians found themselves endeared to wild bayonet charges. The great general Suvorov is known for his love of the bayonet, and is known for his quote: "The bullet is a mad thing; only the bayonet knows what it is about." Realistically this was based on the poor training of the Russian infantry corps which, like the French revolutionaries described by /u/reginaldaugustus, couldn't be relied upon to trade musket volleys with the enemy. I can't quite remember the source at the moment, but I recall that the Russians even performed the only known successful bayonet charge by infantry against cavalry. While successful against poorly trained Ottoman and Polish troops, the Russians were soundly defeated when they faced French regulars.
After the Napoleonic wars the Russians would study Prussia as the epitome of infantry tactics, adopting Prussian traditions like discipline, corporal punishment and parade drilling, while foregoing developments like firing drills and proper weapons training. By the Crimean War, large parts of the Russian army were still fielding muskets (as opposed to the Allied rifles), many of which were had been polished thin enough to be unfireable, supposing that their mechanisms worked and their bearers been trained to use them. At the Battle of Alma the Russians tried charging down hill at the English and French, and were resoundingly slaughtered.
So what I'm getting at is this: infantry tactics made both huge and incremental leaps during the 18th century, but would vary from period, country and battle. While pike was gradually replaced by musket and the general movement was from battles being decided by shock disciplined volley fire, shock tactics would persist and reappear at different times for different reasons.