The words sou, sue sound the same but have different meanings and spellings. Why do sou, sue sound the same even though they are completely different words?
The answer is simple: sou, sue are homophones of the English language.
One of several coins formerly used in France, worth a small amount.
Law To petition (a court) for redress of grievances or recovery of a right.
Law To institute proceedings against (a person) for redress of grievances.
Law To carry (an action) through to a final decision.
To court; woo.
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").