The words politic, politick sound the same but have different meanings and spellings. Why do politic, politick sound the same even though they are completely different words?
The answer is simple: politic, politick are homophones of the English language.
Using or marked by prudence, expedience, and shrewdness; artful.
Using, displaying, or proceeding from policy; judicious: a politic decision.
To engage in or discuss politics.
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").