Roughly speaking, Samprajnata Samadhi refers to conscious or concrete meditation, whereas Asamprajnata Samadhi refers to unconscious or abstract meditation. These terms originate in the First Pada of Patanjali's Yoga Sutras:
1.17. Cognitive meditation is accompanied by reasoning, discrimination, bliss and the sense of 'I am.'
1.18. There is another meditation which is attained by the practice of alert mental suspension until only subtle impressions remain.
Now the Yoga Sutras consist of extremely concise aphorisms, so for more detail on the subject we need to turn to a commentary. Thankfully, the sage Vyasa himself composed a commentary on the Yoga Sutras, the famous Yoga Bhashya. Here is what Vyasa says about the two Sutras above in this excerpt from his Yoga Bhashya:
Question : — " When the agent has suppressed his internal organ
through the two means (just described ), how can the meditation be
said to be Conscious ? "
( Answer ) : —
Sutra (17) : — Conscious, because attended with the forms of
argumentation, deliberation, joy, and egoism.
Com. : —(1)" Argumentation " is the gross perception of the internal
organ, with regard to its object : whereas (2) " Deliberation " is
subtle in its nature. (3) "Joy" is delight. (4) " Egoism " is the
partial cognition of identity....
Now, what is the nature of Unconscious or Abstract meditation and
what are the means to it ?
Sutra (18): — The other, preceded by the practice of the cause of
suspension, is that in which the residua alone remain behind.
Com: — When all the functions have been suspended and the residua
alone remain behind, then we have a suppression of the internal organ,
which constitutes (a form of) meditation, called the Unconscious or
Of this the means is the highest] form of Dispassion (see above).
And, because an exercise based on an object would not be capable of
being fit for its accomplishment, therefore the objectless (or
immaterial) cause of suspension is made the basis here ; and this
cause is devoid of any material object. (Consequently) the internal
organ, preceded by the practice thereof, becomes immaterial, as if
non-existing. This Immaterial or seedless meditation is what is
called the Unconscious or the Abstract.
To sum up, in Samprajnata Samadhi, your attention is from you as an individual onto a particular concrete thing. In Asamprajnata Samadhi, on the other hand, both the sense of individuality disappears as well, and the concrete thing being meditated upon. So it's a more abstract and impersonal experience, and it's highest aspiration it leads to Kaivalya, which I discuss here.