Firms are characterized by production sets or production functions in the standart neoclassical theory of the firm. Ronald Coase enquired into the nature of the firm and observed that, in real world, there are the costs of using the price mechanism and firms are created to economize these costs. This observation has led the rising of the discussions around the conceptual distinction between firms and the market in the theory of the firm. Inspired by this Coasean conceptual distinction, O.Williamson analyzed transaction costs for their efficiency properties and his efforts have caused the birth of transaction cost economics. While accepting the main contributions of Coase to the theory of the firm, some of the works in this research line rejected the conceptual distinction between firms and the market. They assume that market is a universal category, and what we generally call a 'firm' is, in fact, simply a nexus of (market) contracts. In this study, the discussions are classified and assessed around this conceptual distinction and both sides are discussed and compared in detail.