The words meeting, meting sound the same but have different meanings and spellings. Why do meeting, meting sound the same even though they are completely different words?
The answer is simple: meeting, meting are homophones of the English language.
The act or process or an instance of coming together; an encounter.
An assembly or gathering of people, as for a business, social, or religious purpose.
meeting of the minds Agreement; concord.
Present participle of mete.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License and Wordnik.
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").