graphed, graft

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

The answer is simple: graphed, graft are homophones of the English language.

graft
  1. :: noun

    A plant produced by such union.

  2. :: verb-transitive

    To unite (a shoot or bud) with a growing plant by insertion or by placing in close contact.

  3. :: verb-transitive

    To join (a plant or plants) by such union.

  4. :: verb-transitive

    To transplant or implant (living tissue, for example) surgically into a bodily part to replace a damaged part or compensate for a defect.

graphed
  1. :: verb

    Simple past tense and past participle of graph.

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").