The words carol, carrel sound the same but have different meanings and spellings. Why do carol, carrel sound the same even though they are completely different words?
The answer is simple: carol, carrel are homophones of the English language.
A song of praise or joy, especially for Christmas.
An old round dance often accompanied by singing.
To sing in a loud, joyous manner.
To go from house to house singing Christmas songs.
A partially partitioned nook in or near the stacks in a library, used for private study.
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").