Binary fission is the dividing of cells into additional cell bodies. "Binary fusion," though a commonly used phrase, is not a scientific term.
Binary fission is an asexual method of reproduction commonly found in prokaryotic organisms. In the process of binary fission, the organism duplicates its DNA and splits into two parts, each part receiving one copy of the DNA. Some organisms, such as tapeworms, use fission to continuously extend their bodies to grow larger and longer. Other organisms use a type of fission called fragmentation to break off parts of their bodies so that the fragments regenerate to form entirely new beings.