From personal experience, backed-up by a bit of scientific theory, I think there are two ways in which a person might 'nod-off' and take a very short nap:
1. A momentary absence of awareness, as the mind briefly dips-into the shallower type of Deep sleep.
2. A fragmentary micro-dream, as the mind briefly dips into Rapid Eye Movement (REM) sleep.
The 'absence' is what happens when somebody goes to sleep with their head held erect so that the neck muscles are tensed.
Probably, if the person was wired-up to an electroencephalogram, there would be some kind of regular slow wave activity such as occurs in the non-REM or Deep sleep and in petit mal epilepsy (also called absences).
In Deep sleep the voluntary muscles (such as those holding up the head) become relaxed but not completely floppy - they retain muscle tone. So, when somebody who is sitting upright nods-off, their head slowly begins to slump until the person is roused from sleep when the head jerks upright again: giving the notorious 'nodding dog' appearance.
Therefore, unless someone is suffering from narcolepsy, neck muscle tension seems to block a descent from a state of being Awake directly into Dreaming sleep.
(The same applies to other bodily muscles of posture - their tension blocks descent into REM sleep; but it is rare for someone who is standing to nod-off.)
However, if the neck muscles are relaxed, perhaps because the head is hanging forward, or if the head is resting on the hand, or a headrest - then a person can descend from being Awake and directly into Dreaming sleep.
This is possible because Dreaming (or REM) sleep is characterized by flaccid muscle paralysis - a near complete loss of muscle tone; and apparently a posture which maintains muscle tone makes is less likely to move directly into REM sleep, while a position which allows postural muscles to relax enables the mind to dream, instantly.
Subjectively, a brief Deep sleep nap is experienced as an absence - a cessation of awareness and memory; which may mean that sleep is not experienced at all (at least not consciously) - so, with the upright head/ nodding dog type of drowsiness, the person may not know that they have been asleep.
While by contrast a Dreaming sleep nap is experienced as Awareness being interrupted by snatches of dream. The person usually knows they have been asleep, because they recall (albeit perhaps only for a few seconds) the alien, bizarre, non-sequential quality of a dream.
But this is just a fraction of a second, because unless the body is supported, then the onset of flaccid paralysis will rapidly wake the sleeper as his head, body or limbs begin to slump, unresisting.