Homolytic fission: breaking of two or more similar molecules
hetrolytic fission: breaking of two or more different molecules

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Homolytic fission is the chemical bond dissociation of a neutral molecule where two electrons that are involved in the bond formation are distributed equally among the two species. It generates two free radicals. 
But Heterolytic fission involves dissociation of a bond between two elements in which the two electrons involved in bond formation remain with only one of the two participating elements.