The words stationary, stationery sound the same but have different meanings and spellings. Why do stationary, stationery sound the same even though they are completely different words?
The answer is simple: stationary, stationery are homophones of the English language.
Not capable of being moved; fixed.
Unchanging: a stationary sound.
One that is stationary.
Writing materials and office supplies.
Writing paper and envelopes.
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.