我在wordreference查了一下
hire purchase：
Hire purchase is a sort of leasing arrangement under which once all the periodic payments have been made,the customer takes ownership of the equipment.
强调的是leasing arrangement,是一种租赁关系,而租者拥有租赁期间的是用权.
on installments
更侧重于购买的分期付款,比如购房首付分期什么的~
租者拥有产权
希望回答对你有用