The words gaze, gays sound the same but have different meanings and spellings. Why do gaze, gays sound the same even though they are completely different words?
The answer is simple: gaze, gays are homophones of the English language.
Plural form of gay.
To look steadily, intently, and with fixed attention.
A steady, fixed look.
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.
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").