greave, grieve

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

The answer is simple: greave, grieve are homophones of the English language.

greave
  1. :: noun

    Leg armor worn below the knee. Often used in the plural.

grieve
  1. :: verb-transitive

    To cause to be sorrowful; distress: It grieves me to see you in such pain.

  2. :: verb-transitive

    To mourn or sorrow for: We grieved the death of our pastor.

  3. :: verb-transitive

    Usage Problem To file an official or formal grievance on account of (an actual or perceived injustice).

  4. :: verb-transitive

    Archaic To hurt or harm.

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").