cougher, coffer

The words cougher, coffer sound the same but have different meanings and spellings. Why do cougher, coffer sound the same even though they are completely different words?

The answer is simple: cougher, coffer are homophones of the English language.

coffer
  1. :: noun

    A strongbox.

  2. :: noun

    Financial resources; funds.

  3. :: noun

    A treasury: stole money from the union coffers.

  4. :: noun

    Architecture A decorative sunken panel in a ceiling, dome, soffit, or vault.

cougher
  1. :: noun

    A person who coughs.

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").