The words sic, sick sound the same but have different meanings and spellings. Why do sic, sick sound the same even though they are completely different words?
The answer is simple: sic, sick are homophones of the English language.
Thus; so. Used to indicate that a quoted passage, especially one containing an error or unconventional spelling, has been retained in its original form or written intentionally.
To set upon; attack.
To urge or incite to hostile action; set: sicced the dogs on the intruders.
Suffering from or affected with a physical illness; ailing.
Of or for sick persons: sick wards.
Nauseated.
Mentally ill or disturbed.
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").