The words courtesy, curtesy sound the same but have different meanings and spellings. Why do courtesy, curtesy sound the same even though they are completely different words?
The answer is simple: courtesy, curtesy are homophones of the English language.
A polite gesture or remark.
Consent or agreement in spite of fact; indulgence: They call this pond a lake by courtesy only.
Willingness or generosity in providing something needed: free advertising through the courtesy of the local newspaper.
The life tenure that by common law is held by a man over the property of his deceased wife if children with rights of inheritance were born during the marriage.
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.