The words wort, wart sound the same but have different meanings and spellings. Why do wort, wart sound the same even though they are completely different words?
The answer is simple: wort, wart are homophones of the English language.
A hard rough lump growing on the skin, caused by infection with certain viruses and occurring typically on the hands or feet.
A similar growth or protuberance, as on a plant.
A genital wart.
One that resembles or is likened to a wart, especially in unattractiveness or smallness.
A plant. Often used in combination: liverwort; milkwort.
An infusion of malt that is fermented to make beer.
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").