The words fuhrer, furor, furore sound the same but have different meanings and spellings. Why do fuhrer, furor, furore sound the same even though they are completely different words?
The answer is simple: fuhrer, furor, furore are homophones of the English language.
Alternative spelling of führer.
A general commotion; public disorder or uproar.
Violent anger; frenzy.
A fashion adopted enthusiastically by the public; a fad.
A state of intense excitement or ecstasy.
Chiefly British Variant of furor.
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").