The words rang, wrang sound the same but have different meanings and spellings. Why do rang, wrang sound the same even though they are completely different words?
The answer is simple: rang, wrang are homophones of the English language.
Past tense of ring2.
An obsolete or dialectal (Scotch) form of wrong.
An obsolete or provincial preterit of wring.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from The Century Dictionary and Cyclopedia 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").