The words weaner, weiner sound the same but have different meanings and spellings. Why do weaner, weiner sound the same even though they are completely different words?
The answer is simple: weaner, weiner are homophones of the English language.
An animal that has been recently weaned.
A device used to help wean a young animal by keeping it from suckling.
Common misspelling of wiener.
Definitions 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").