Both binary fission and multiple fission are asexual reproduction and occur with the presence of only one parent.
Binary fission consists of divisions of the nucleus followed by the division of cytoplasm producing two cells each having a daughter nucleus.
Example – Amoeba
In multiple fission, the nucleus of the parent cell undergoes repeated divisions to produce many daughter nuclei. The cytoplasm also divides and cleaves around each nucleus forming several daughter cells in the parent cell. In favourable conditions when the parent cell membrane raptures all the daughter individuals are released.
Example – Plasmodium