The words sigher, sire sound the same but have different meanings and spellings. Why do sigher, sire sound the same even though they are completely different words?
The answer is simple: sigher, sire are homophones of the English language.
One who sighs.
The male parent of an animal, especially a domesticated mammal such as a horse.
Archaic A male ancestor; a forefather.
Archaic A gentleman of rank.
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.