The words hair, hare sound the same but have different meanings and spellings. Why do hair, hare sound the same even though they are completely different words?
The answer is simple: hair, hare are homophones of the English language.
Any of the cylindrical, keratinized, often pigmented filaments characteristically growing from the epidermis of a mammal.
A growth of such filaments, as that forming the coat of an animal or covering the scalp of a human.
A filamentous projection or bristle similar to a hair, such as a seta of an arthropod or an epidermal process of a plant.
Fabric made from the hair of certain animals: a coat of alpaca hair.
Any of various mammals of the family Leporidae, especially of the genus Lepus, similar to rabbits but having longer ears and legs and giving birth to active, furred young.
To move hurriedly, as if hunting a swift quarry.
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.