theirs, there's

The words theirs, there's sound the same but have different meanings and spellings. Why do theirs, there's sound the same even though they are completely different words?

The answer is simple: theirs, there's are homophones of the English language.

theirs
  1. :: pronoun

    Used to indicate the one or ones belonging to them: The red house is theirs. If your car doesn't start, take theirs.

  2. :: pronoun

    Usage Problem His or hers: brought his own lunch and expected everybody else to bring theirs. See Usage Notes at he1, they.

there's
  1. :: phrase

    contraction of there is

  2. :: phrase

    contraction of there has

  3. :: phrase

    contraction of there are See there're.

Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License and Wordnik.

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About Homophones

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").