Manufacturing costs are the costs of direct materials, plus the cost of employees directly involved in production, plus manufacturing overhead (such as depreciation of equipment, factory rent and utility bills, maintenance and repair costs, costs of supervisory staff).
For internal management accounts, production costs are usually all costs incurred in the manufacturing facilities, and are sometimes also called manufacturing costs.
US GAAP accounting rules require external financial statements to assign all manufacturing costs to units produced. The resulting unit costs are used for both inventory valuation, and to calculate the cost of goods sold.