Regulated and Unregulated? LED

What does it mean for an LED flashlight to be regulated, or unregulated?

How does it affect these situations?

A) Flashlight with 3.7 to 6.0V lamp, using 3.7V 18650 battery (2200mAh)?
runtime 110 minutes regulated, 30 minutes unregulated?

B) Flashlight with 3.7 to 13V lamp, using 2X 3.7 18500 batteries (each at 1500mAh)? runtime 160 minutes regulated output, unregulated???

These flashlights are in no way comparable, but their curves are typical of regulated, and non-regulated LED flashlights. Look at the runtime graph for each.

The Inova X1 is non-regulated. It constantly dims as the battery is used up.
http://www.flashlightreviews.com/reviews/inova_x1.htm

The Fenix P1 has very good regulation, as do most Fenix lights. It's circuity provides a constant current to the LED until there is simply not enough power left for the circuity to function in regulation. This provides the same level of light for most of the time you are using the flashlight. However, there is the risk of some flashlights simply blinking out when the battery is dead.
http://www.flashlightreviews.com/reviews/fenix_p1.htm


Another thread with the same question is here:
https://www.candlepowerforums.com/threads/173963