NOT ISSUED banknotes in most of the cases are available on the market. Somehow part of that banknotes slipped out from the printer, national bank or others who get them printed before it was decided for any reason not to be released into circulation.
The most important condition to call a banknote NOT ISSUED is that it must be an official banknote aproved and designed by the authorities.
Otherwise it is a fantasy, privat issue.
That is also a very usefull field to filter banknotes. Many collectors are interested only in banknotes that were used in circulation. “Not issued” banknotes are often very expencive and also UNC grade most of the time.
“Remainder” is a term not used all over the world and it is not the same as NOT ISSUED banknote. There is a very big difference. As I know, remaiders are banknotes that were left in the printer or national bank treasury for different reasons like banknotes with missing signatures, missing serial number… A stock of banknotes left in the storage and never left in circulation.
“Not circulating” banknotes and also something else. Some states issue commemorative banknotes that are sold only in folders and are not released for circulations but only to sell to collectors like the “non circulating” coins.
For all other types of banknotes it is easy as they can be listed as a variety in year lines; specimens, replacement notes, remainders, notes with some errors… Because the design and the P# is always the same, maybe with an addition, for example P#14, P#14a, P#14s…