meeter, meter

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

The answer is simple: meeter, meter are homophones of the English language.

meeter
  1. :: noun

    One who meets.

  2. :: adjective

    comparative form of meet: more meet

meter
  1. :: noun

    The measured arrangement of words in poetry, as by accentual rhythm, syllabic quantity, or the number of syllables in a line.

  2. :: noun

    A particular arrangement of words in poetry, such as iambic pentameter, determined by the kind and number of metrical units in a line.

  3. :: noun

    The rhythmic pattern of a stanza, determined by the kind and number of lines.

  4. :: noun

    Music Division into measures or bars.

Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, 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").