The words mews, muse sound the same but have different meanings and spellings. Why do mews, muse sound the same even though they are completely different words?
The answer is simple: mews, muse are homophones of the English language.
An alley where there are stables; a narrow passage; a confined place.
A place where birds of prey are housed.
Plural form of mew.
Third-person singular simple present indicative form of mew.
To be absorbed in one's thoughts; engage in meditation.
To consider or say thoughtfully: mused that it might take longer to drive than walk.
A state of meditation.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, 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.