The words patience, patients sound the same but have different meanings and spellings. Why do patience, patients sound the same even though they are completely different words?
The answer is simple: patience, patients are homophones of the English language.
The capacity, quality, or fact of being patient.
Chiefly British The game solitaire.
The capacity, quality, or fact of being patient.
Chiefly British The game solitaire.
Plural form of patient.
Plural form of patient.
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").