Lancers Dragoons and Cavalry

Or in America, Cavalry... because any soldier on a horse is cavalry.

But out west the cavalry is more accurately described as dragoons.

Dragoons are mounted infantry, that is they ride up to where the battle will take place, dismount and fight.

Cavalry stays mounted for the battle.

Lancers are cavalry who use a spear or lance instead of a saber.

In the US it's muddied because we issued a saber to our dragoons and called them cavalry.  I am sure there were some Civil War vets who grumbled that things were different in the old Cav.

In Europe the lines were more sharply drawn.  Dragoons got carbines or short rifles and a bayonet.  Lancers got a spear they called a lance and may or may not have gotten a carbine.  Cavalry got a carbine and a saber.

At one point there was a different long arm for each of them (although lancers and cavalry tended to share rifle designs), and another for the cannon cockers.

It was all of these fine distinctions that drove England to the idea of a short rifle, or one rifle for all troops, infantry, artillery, cavalry, dragoons...  That became the Short Magazine Lee Enfield derived from the much longer Lee-Metford.

The short rifle idea really caught on and by WW2 everyone was doing it.

Another funny bit is modern mechanized infantry are also something of dragoons.  They ride up to where the fight is, dismount and fight.