The words close, clothes sound the same but have different meanings and spellings. Why do close, clothes sound the same even though they are completely different words?
The answer is simple: close, clothes are homophones of the English language.
Being near in space or time. See Usage Note at redundancy.
Being near in relationship: close relatives.
Bound by mutual interests, loyalties, or affections; intimate: close friends.
Having little or no space between elements or parts; tight and compact: a close weave.
Articles of dress; wearing apparel; garments.
Bedclothes.
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").