The words troop, troupe sound the same but have different meanings and spellings. Why do troop, troupe sound the same even though they are completely different words?
The answer is simple: troop, troupe are homophones of the English language.
A group or company of people, animals, or things. See Synonyms at band2, flock1.
A group of soldiers.
Military units; soldiers.
A unit of cavalry, armored vehicles, or artillery in a European army, corresponding to a platoon in the U.S. Army.
A company or group, especially of touring actors, singers, or dancers. See Synonyms at band2.
To tour with a theatrical company.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.