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Probably an oversimplification, but it depends on what word you are negating. To negate the noun, kein is used. To negate the verb or adjective, nicht is used. When you are stating "A is not B.", with A and B being nouns, you always use kein. If B is an adjective, you would use nicht.
Keine is the plural or feminine form of kein. There are other forms such as keinen, keiner, keines, dpending on gender and case.