Does the increase or decrease of the Interest rate (coupon rate) of bonds have the same effect as rising or falling interest rate of the central bank on the economy? In other words when we say that Interest rate is rising or falling then are we referring to the interest rate of the bond or the interest of the central bank?
"Interest rate" associated with a bond, or more precisely, yield, is not the same as the coupon rate. Coupon rate is the percentage of par/face value of the bond that is paid out periodically. The yield of a bond is the discount rate with which one discounts the cash flows associated with the bond taking into account the timings of the cash flows such that the sum of the discounted cash flows equals the price of the bond. The price and yield of a bond have an inverse relationship.
When they say interest rates are rising, it is the fed funds rate that they are referring to. It is the interest rate which banks charge each other to lend federal funds overnight. This rate influences the general level of interest rates in the market - basically the cost of borrowing money. The Fed raises this rate, for example, when they want to control inflation, by selling its securities to member banks reducing the available funds these banks have for lending to other banks so that they can raise their lending rates owing to money having become scarce. That makes borrowing expensive but controls inflation because people can't borrow easily and spend.
When the Fed wants to stimulate the economy it reduces this rate by buying securities from member banks increasing their available funds for lending forcing banks to reduce their lending rates. This reduces the general level of interest rates, and allows people to borrow more to invest or to spend and stimulates the economy.
Whenever the Fed buys bonds/securities their prices rise, and yields fall, and vice versa. So the Fed uses this buying and selling as a tool to control yields/interest rates.