The words typhous, typhus sound the same but have different meanings and spellings. Why do typhous, typhus sound the same even though they are completely different words?
The answer is simple: typhous, typhus are homophones of the English language.
Of or pertaining to typhus; of the nature of typhus.
Any of several forms of infectious disease caused by rickettsia, especially those transmitted by fleas, lice, or mites, and characterized generally by severe headache, sustained high fever, depression, delirium, and the eruption of red rashes on the skin. Also called prison fever, ship fever, typhus fever.
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").