A troop is a group — most often military, and also used of scouts and of some animals. A troupe is a company of performers: a dance troupe, a troupe of actors. The E marks the theatrical one, and both come from the same French word.
The core difference
Same origin, split by what the group does.
- troop — a group, usually military: troop movements. Also a scout troop, a troop of baboons.
- troupe — a company of performers: a circus troupe.
The plural point
Troops in military reporting means individual soldiers — "200 troops" is 200 people, not 200 units. That usage is well established but occasionally causes confusion, because a troop as a formal unit is a specific body of soldiers, typically cavalry or armour.
The related word
Trouper — as in "a real trouper" — comes from the theatrical sense: someone who keeps performing regardless. It is often written trooper, which is a soldier. Both spellings exist and mean different things.