In America, the popularity of rebates comes from a time (I think maybe in the 1970s) when government temporarily froze wages and prices to try to help the economy. Costs to manufacture goods continued to rise, but manufacturers were unable to charge more to cover those rising costs, so profits fell. The solution was to charge a higher initial price which would cover possible cost increases (in case this happened again), and "rebate" down to the actual net retail price paid by the consumer.
Rebates also function as a marketing tool: It feels like you're getting money for nothing. The rebate can be offered as cash for a big-ticket item (the classic example is a car) which is financed by a long-term loan.
A refund usually means getting all of your money back- typically because of some dissatisfaction or defect in the product/service. Usually, this involves the physical return of the item to the seller, but not always. Sometimes the cost or hassle of returning the item is greater than the value of that item. Sometimes it's a gesture of good will on the part of the seller, and of course it's impossible to reverse a service already performed.