The words cyst, cist sound the same but have different meanings and spellings. Why do cyst, cist sound the same even though they are completely different words?
The answer is simple: cyst, cist are homophones of the English language.
A wicker receptacle used in ancient Rome for carrying sacred utensils in a procession.
A stone-lined grave, especially a tomb consisting of a pit lined with stones and often having a lid of stone or wood.
Pathology An abnormal membranous sac containing a gaseous, liquid, or semisolid substance.
Anatomy A sac or vesicle in the body.
Biology A small capsulelike sac that encloses certain organisms in their dormant or larval stage.
Botany A thick-walled resting spore, as in certain algae or fungi.
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.