The words vice, vise sound the same but have different meanings and spellings. Why do vice, vise sound the same even though they are completely different words?
The answer is simple: vice, vise are homophones of the English language.
A jester or buffoon.
An evil, degrading, or immoral practice or habit.
A serious moral failing.
Wicked or evil conduct or habits; corruption.
A clamping device, usually consisting of two jaws closed or opened by a screw or lever, used in carpentry or metalworking to hold a piece in position.
To hold or compress in or as if in a vise.
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").