What type of fission results in one atom receiving both of the shared electrons, creating ions?

Heterolytic fission is the correct type of fission described in the question. During this process, a covalent bond breaks and one atom retains both of the electrons involved in the bond, leading to the formation of an anion, while the other atom becomes a cation due to the loss of its electron. This results in the creation of charged ions, which are crucial in various chemical reactions, particularly in polar solvent systems where such ionization significantly affects reactivity and stability.

In contrast, homolytic fission involves the equal sharing of the bonding electrons between the two atoms, leading to the formation of two free radicals, which do not carry a charge and are quite different in terms of their reactivity and properties compared to ions formed through heterolytic fission. Radical fission is not a standard term used in chemistry; rather, it may mistakenly refer to homolytic fission. Exothermic fission does not refer to the manner in which bonds break but rather indicates the energy change involved in the reaction process, which is not the focus of this question.