Money, as part of economics, is a symbolic agreed valued medium for the exchange or trade of goods and/or services. Paraphrased from Homer Simpson like in this youtube clip

Currency is the specific type of money that is in circulation with varying agreed upon values in comparison to another currency. For example a US Dollar is a currency, a Swiss Franc is a currency, a bitcoin is currency.

Money can also be viewed as a form of debt, as stated on the US dollar bill. "This note is legal tender for all debts, public and private". 


An image of a banknote  representing US currency of  $1 dollar. image: US Treasury, U.S Bureau of Engraving and Printing.

Banknotes, bills,  and or coinage is an economic technological design solution to moving or transporting money from one place to another or from individuals or groups within a society.

The storage and distribution of money in society is typically managed by special economic institutions.

Money has a social dimension

Money has a very significant social value. The more money an individual or company has the higher potential social standing or influences  they have. In addition access to more amounts of money allow for greater choices in goods and or services they have. This leads to concepts of wealth and poverty. This is also the basis of social standing and desirability in some cultures.

Biological analogy

In a biological system like a cell, there are specialised molecules for carrying energy called ATP. The purpose of this molecule is for the exchange of goods(storage, e.g. transport into a vesicle) or services (physical movement) in a cell. This process is called metabolism.

ATP (Adenosine triphosphate) is a specialised biological molecule for exchanging energy within living cells. image: wikipedia

A slight different feature of ATP vs real money is that ATP actually carries a large potential energy source, it's value is chemical energy in nature. Real money, such as notes/currency has no physical value due to a more complex series of social and energy distribution agreements for what money has a value for.  Although ultimately even in economics a limiting factor is energy accessibility.