lux, luxe

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

The answer is simple: lux, luxe are homophones of the English language.

lux
  1. :: noun

    The International System unit of illumination, equal to one lumen per square meter. See Table at measurement.

luxe
  1. :: noun

    The condition of being elegantly sumptuous.

  2. :: noun

    Something luxurious; a luxury.

Definitions from The American Heritage® Dictionary of the English Language, 4th Edition 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").