The words missed, mist sound the same but have different meanings and spellings. Why do missed, mist sound the same even though they are completely different words?
The answer is simple: missed, mist are homophones of the English language.
Simple past tense and past participle of miss.
A mass of fine droplets of water in the atmosphere near or in contact with the earth.
Water vapor condensed on and clouding the appearance of a surface.
Fine drops of a liquid, such as water, perfume, or medication, sprayed into the air.
A suspension of fine drops of a liquid in a gas.
Definitions from Wiktionary, Creative Commons Attribution/Share-Alike License, 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.