The words waisted, wasted sound the same but have different meanings and spellings. Why do waisted, wasted sound the same even though they are completely different words?
The answer is simple: waisted, wasted are homophones of the English language.
Having a waist or a part like a waist.
Having a waist of a specified kind: high-waisted; slim-waisted.
Not profitably used or maintained: a wasted inheritance.
Needless or superfluous: These are wasted words.
Deteriorated; ravaged: a wasted landscape.
Frail and enfeebled, as from prolonged illness; emaciated.
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").