The story
The great night is the one everybody knows, and the monthly one is what makes it a practice rather than an anniversary. The dark fourteenth is the last night before the moon disappears, and the tradition answers the thinnest moon of every month the same way it answers the thinnest of the year: by staying awake.
The Śiva Purāṇa makes no distinction between them in what is done — only in scale. What is kept through four watches in Māgha is kept through one or two in the other months, by whoever keeps it.
For many it is the trial run that makes the great night possible, and for some it is the whole of their practice.