Besides the "awake", "asleep", and "off" states that @CommonsWare mentioned, there is the distinction between whether the CPU is asleep, or just the screen is. For example, the official docs here describe it this way:
To avoid draining the battery, an Android device that is left idle
quickly falls asleep. However, there are times when an application
needs to wake up the screen or the CPU and keep it awake to complete
some work. [emphasis added]
In the three-stage framework that CommonsWare described, a device whose screen is dark is probably not categorized as "asleep" unless the CPU is also stopped. But as the above paragraph implies, the screen-dark state can legitimately be referred to as "asleep." No doubt this is why people refer to "deep sleep" to clarify that they're talking about the CPU being asleep.
This doc page also mentions
When an Android device is left idle, it will first dim, then turn off
the screen, and ultimately turn off the CPU. This prevents the
device's battery from quickly getting drained.
So if you want to be comprehensive, you could add "dim" to the list of "sleep stages/levels":
- awake
- dim
- screen off
- CPU off (true "sleep" or "deep sleep")
- power off
Apparently the transition from 2 to 3 to 4 is pretty fast when the idle timeout occurs. But there are other times when the screen can be off without a transition to deep sleep; e.g. when playing audio (at least in certain apps).
I wish I could tell you how to predict when the device will transition from screen off to CPU off -- e.g. how long the timeout is -- but I haven't found that information. What I have found is FLAG_KEEP_SCREEN_ON and WAKE_LOCK to prevent one or the other from happening.
P.S. If you want to be exhaustive, you could count daydream in your list of "sleep stages":
Daydream is a new [as of Android 4.2] interactive screensaver mode for Android devices. It
activates automatically when the device is inserted into a dock or
when the device is left idle while plugged in to a charger (instead of
turning the screen off).
From the point of view of the previously-running app, it sounds like daydream behaves like switching to a different app. So it's not really a matter of the device sleeping, though your activity does get stopped, I would assume.