The purpose of this study is to establish the theoretical foundation on which we can understand the difference between the standard monetary system and the fiat money system, by focusing the accessibility to the medium of exchange. We analyzed the economic cost and economic distance to travel from the initial point (=before conducting the exchange) to the desired situation (=after the exchange). We concluded that the standard-goods should not be selected from the goods with high intrinsic value because they help improve the real economic activities. This clarifies the reason for the transition of the money from ancient times to modern ages. However, when one of real goods is selected as a monetary standard, opportunity cost of the monetary-use is inevitable, even if its intrinsic value is small. This determines the upper limit of efficiency of standard money system. On the other hand, an inconvertible paper money, purely nominal, doesn't generate such an opportunity cost, because it is not based on any real goods. In this sense, there is a difference between fiat and standard money.