Banknote. – A piece of paper issued by a bank (public or private) representing its promise to pay a specific sum to the bearer on demand and acceptable as money.
Bill.- a piece of paper money (especially one issued by a central bank).
Currency. – From the Latin currens (to run or flow) i.e., a constant movement of money from person to person. Circulating paper money.
Legal tender. – notes that are still used as money in the country of issue.
Money.- from the Latin moneta , any written or stamped promise, certificate, or order, as a government note, a bank note, a certificate of deposit, etc., which is payable in standard coined money and is lawfully current in lieu of it; in a comprehensive sense, any currency usually and lawfully employed in buying and selling.
Notaphily. – From the Latin nota “note” and the Greek philos “love”. The term notaphilist is used for paper money collectors.
Note. – A piece of paper currency.
Numismatics. – The study or collection of money, coins, and often medals.
Paper money. – Any type of currency printed on paper. These term also includes all the various materials that have served as paper substrates and surrogates trough the ages. Nowadays for instance the polymer notes.