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.
One who meets.
comparative form of meet: more meet
The measured arrangement of words in poetry, as by accentual rhythm, syllabic quantity, or the number of syllables in a line.
A particular arrangement of words in poetry, such as iambic pentameter, determined by the kind and number of metrical units in a line.
The rhythmic pattern of a stanza, determined by the kind and number of lines.
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.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.