The words council, counsel sound the same but have different meanings and spellings. Why do council, counsel sound the same even though they are completely different words?
The answer is simple: council, counsel are homophones of the English language.
An assembly of persons called together for consultation, deliberation, or discussion.
A body of people elected or appointed to serve as administrators, legislators, or advisors.
An assembly of church officials and theologians convened for regulating matters of doctrine and discipline.
The discussion or deliberation that takes place in such an assembly or body.
The act of exchanging opinions and ideas; consultation.
Advice or guidance, especially as solicited from a knowledgeable person. See Synonyms at advice.
A plan of action.
Private, guarded thoughts or opinions: keep one's own counsel.
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").