The words cite, sight, site sound the same but have different meanings and spellings. Why do cite, sight, site sound the same even though they are completely different words?
The answer is simple: cite, sight, site are homophones of the English language.
To quote as an authority or example.
To mention or bring forward as support, illustration, or proof: cited several instances of insubordinate behavior.
To commend officially for meritorious action in military service.
To honor formally.
The ability to see.
The act or fact of seeing: hoping for a sight of land; caught sight of a rare bird.
Field of vision.
The foreseeable future; prospect: no solution in sight.
A website.
The place where a structure or group of structures was, is, or is to be located: a good site for the school.
The place or setting of something: a historic site; a job site.
To situate or locate on a site: sited the power plant by the river.
Definitions 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").