The words stair, stare sound the same but have different meanings and spellings. Why do stair, stare sound the same even though they are completely different words?
The answer is simple: stair, stare are homophones of the English language.
A series or flight of steps; a staircase. Often used in the plural.
One of a flight of steps.
To look directly and fixedly, often with a wide-eyed gaze. See Synonyms at gaze.
To be conspicuous; stand out.
To stand on end; bristle, as hair or feathers.
To look at directly and fixedly: stared him in the eyes.
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.