The demand for central-bank money:

The demand for central-bank money is the sum of currency demand by the public and reserve demand by the banking system. here, the supply of central bank money is under the direct control of the central bank.

Demand for central-bank money = Currency demand by the public + Reserve demand by the banking system.

Demand for money:

The demand for money refers to how much assets individuals wish to hold in the form of mone(cash or bank deposits rather than investments). It is sometimes referred to as liquidity preference. There are three types of demand for money- Transaction demand (for buying and selling of goods and services), money needed for financial emergencies (in case of losing job, health emergency etc), and speculative demand or demand for buying securities to get benefits or profits. When iterest rate increase demand for money decrease and vice-versa. When interest rate increase then people spend less and invest more to get higher rate of return.

A set A is a subset of another set B if all elements of the set A are elements of the set B. The Demand for Money(Md) is a suset of  the Demand for Central Bank Money (Hd). HD is a wider concept than Md. Md is a part of HD.

HD = Md + Reserve demand by the banking system.

During the economic boom demand for money is high because people spend more and demand for money for the speculation. During the boom phase market perform better and its creat a lot of speculative opportunities for the speculators. Other side in case of the Demand for Central Bank Money (Hd) the banking system demand for more money to fulfill the RR. The demand for RR is when the central bank increase reserve ratio or the deposits liabilities of the bank increase. When the interest rate is low the  Demand for Central Bank Money (Hd) by the banking system is high and vice-versa. Bank fulfill this demand in interbank market and federal fund rate affect it. The amount of reserve required by a bank depends on the habits of the customers and the business conditions of the locality, which the bank is serving also. During the growing pase or a boom phase of the economy the confidence level of consumers and investors are high and they consume and invest more that increase borrowing and increasing borrowing, increase lending also. To fulfill the demand of borrowing bank need more fund and increase demand for reserve.