The words mucous, mucus sound the same but have different meanings and spellings. Why do mucous, mucus sound the same even though they are completely different words?
The answer is simple: mucous, mucus are homophones of the English language.
Containing, producing, or secreting mucus: a mucous tissue.
Relating to, consisting of, or resembling mucus: a mucous substance.
The viscous, slippery substance that consists chiefly of mucin, water, cells, and inorganic salts and is secreted as a protective lubricant coating by cells and glands of the mucous membranes.
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").