The words autarchy, autarky sound the same but have different meanings and spellings. Why do autarchy, autarky sound the same even though they are completely different words?
The answer is simple: autarchy, autarky are homophones of the English language.
Absolute rule or power; autocracy.
A country under such rule.
Variant of autarky.
A policy of national self-sufficiency and nonreliance on imports or economic aid.
A self-sufficient region or country.
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.