Cavalry 
Light Cavalry
At this point cavalry was light, most army leaders preferred to have big horses for a prestige. The main role of cavalry was as shock troops, charge the enemy and frighten them so that they get into disarray. As defense the where used to harass the enemy. And offcourse to brake the enemy so that the infantry would come in ( more or less the same as in the middle ages)
Cavalry was most effective against infantry when they were on the move or in a single line formation (consisting of less than 4 lines)
Dragoons
Dragoons where the most common type. They rode horses as an extra, to get from one place to the other quickly. Because of the difficult way to fire the muskets they mostly got of the horse to fire. They were mostly equipped with a sabre, axe and a musket. But didn’t have much chance against through cavalry.
later they changed the equipment and became more like cavalry men this was around the Napoleonic wars. These Dragoons rode larger horses than the light cavalry and wielded straight, rather than curved swords. Napoleon was a master with his dragoons, later it was turned against him at the battle of Waterloo, (also because the general of the dragoons made a wild charge into fresh troops)
later the dragoons where converted to Hussars and Lancers
Cuirassiers,
Equipped with armour and firearms, they were the successors of the medieval knights, I’m not certain if they had a huge benefit against rifle infantry (the plating a mean) but they had a major benefit against other types of cavalry
By the end of the 19th century the Cuirassiers where fading and become more as heavy Dragoons (or the Dragoons became more like them)
Light Lancers
Basic cavalry but had a lance and sword ;)
Especially useful against infantry static or moving but they were less and less used because of the advantages of gunpowder especially after the French revolution.
there are some others but these I think where the most used
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