The words worst, wurst sound the same but have different meanings and spellings. Why do worst, wurst sound the same even though they are completely different words?
The answer is simple: worst, wurst are homophones of the English language.
Most inferior, as in quality, condition, or effect.
Most severe or unfavorable.
Being furthest from an ideal or a standard; least desirable or satisfactory.
In the worst manner or degree.
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").