The words councillor, councilor, counsellor, counselor sound the same but have different meanings and spellings. Why do councillor, councilor, counsellor, counselor sound the same even though they are completely different words?
The answer is simple: councillor, councilor, counsellor, counselor are homophones of the English language.
Variant of councilor.
A member of a council, as one convened to advise a governor. See Usage Note at council.
Alternative spelling of counselor.
A person who gives counsel; an adviser.
An attorney, especially a trial lawyer.
A person who supervises young people at a summer camp. See Usage Note at council.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License 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").