What is the difference between a loan and an installment sale in terms of permissibility or prohibition according to Islamic law?

There is a significant difference between selling by installment and a loan. A loan is a gratuitous contract, intended for assistance, while a sale is a commutative contract, intended for benefit and profit. An increase in the price of a commodity in exchange for deferment is permissible, whereas an increase in a loan over the principal is forbidden because it contradicts the purpose of assistance.