Actually the two terms are used in two different contexts.
Ordinary course of business: This covers the usual transactions, customs and practices of a certain business. This concept is most used to confirm that the transactions being entered into by a business are genuine.
For example a firm has a high demand for its products and sells against advance payment only. If such a firm allows discount to some party, will it raise some eyebrows? Such a transaction is not in the ordinary course of business. In such cases the management needs to investigate such transactions.
Operating Activities: These are the company's core business activities, such as manufacturing, distributing, marketing and selling a product or service. Operating activities should generally provide the majority of a company’s cash flows. This concept is mainly used to gauge the real profitability of a business. This is so because sometimes non-operating incomes/expenses have a significant impact on net profit/loss of a firm. So in such a case we need to segregate the expenses and incomes from non-operating activities. Normally investing and financing activities are considered non-operating activities.