The words mandrel, mandrill sound the same but have different meanings and spellings. Why do mandrel, mandrill sound the same even though they are completely different words?
The answer is simple: mandrel, mandrill are homophones of the English language.
A spindle or an axle used to secure or support material being machined or milled.
A metal rod or bar around which material, such as metal or glass, may be shaped.
A shaft on which a working tool is mounted, as in a dental drill.
A large fierce baboon (Papio sphinx syn. Mandrillus sphinx) of western Africa, having a beard, crest, and mane and brilliant blue, purple, and scarlet facial markings in the adult male.
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").