The words coarse, corse, course sound the same but have different meanings and spellings. Why do coarse, corse, course sound the same even though they are completely different words?
The answer is simple: coarse, corse, course are homophones of the English language.
Of low, common, or inferior quality.
Lacking in delicacy or refinement: coarse manners.
Vulgar or indecent: coarse language.
Consisting of large particles; not fine in texture: coarse sand.
Archaic A corpse.
Onward movement in a particular direction; progress: the course of events.
Movement in time; duration: in the course of a year.
The direction of continuing movement: took a northern course.
The route or path taken by something, such as a stream, that moves. See Synonyms at way.
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.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").