In general, most schools of Buddhism recognize these levels of concentration. These are preparation or momentary, neighborhood or access, and fixed or full concentration. This is from commentaries, not the Discourses. However, the concept can likely be inferred from the Discourses.
Simply put, most people have fleeting moments of concentration. To do anything sustained, one must get past the Five Blocks or Hindrances. The 5 are sensuality, enmity, apathy, angst, and suspicion. Once we can suspend those for 20 minutes or so, we can reach access samadhi. The danger lies 'there,' in access concentration. Some people have visionary experiences at this level. For some, these can be strange or frightening. Others might get infatuated, or attach too much significance to these 'charisms.'
An article I found on line, "Meditation - The Interesting Quirks of Access Samadhi" is useful.
The important thing, in samatha meditation, is to get beyond access concentration into the meditative absorptions, the rupa jhanas. That is the next level.
Picture an elevator. You have noticed that the elevator exists; and the door opens, but you do not get on board. You start thinking about entering. That is like fleeting or momentary concentration. You finally get past your trepidations and get on board. You ride up and the door opens; but you do not get off. You might be frightened about or marveling at the thrill of the ride. That is like access concentration.
The first floor is the first absorption. This is the same as the first meditative heaven, or the first Brahma Heaven. It has five qualities:
- Directed or applied attention and investigation.
- Arousal of interest and sustained attention.
- The mood of fleeting mental joyousness, delight, or rapture.
- A more sustained feeling of bliss, or contentment,
- One-pointed-ness of concentration.
The arising of these 5 is like getting off the elevator. As the ascending elevator stops, and the door to the first jhana opens, there can be sinking feeling. That can be another danger point.