A letter of demand is sent when a party is owed money by a business, and money remains unpaid despite attempts to collect it. It often foreshadows legal proceedings if the receipt of the letter still fails to produce payment.
A statutory demand is sent to a debtor company (someone that owes you). While it can help to recover your money, it is not really designed to be a debt recovery tool. It can, however, become a real incentive for your debtor to pay their debts.