I would have to say that regulated just means that the power from the batteries is being altered in some form to provide whatever power to the bulb/led the designer desired. It could be to bump up the about 1.2-1.5V of a AA battery to 3.4V for an LED
A battery can be boosted (voltage step-up) or bucked (voltage step-down) without being regulated. For example, a common scheme is to simply triple battery voltage for AA lights, in order to step up ~1.2V up to the ~3.6V needed to drive the LED. The output curve will still decay with the battery discharge curve in that case.
In order for a light to be truly regulated, it must have some form of feedback -- that is a circuit that adjusts the gain of the voltage step-up, or step-down circuit based on measurement of the actual output.
Some lights are fully-regulated buck-boost, that is, they will step-up, OR step-down voltage so as to maintain constant output. Often these include low battery voltage warning features as well so that the light doesn't suddenly go dead without warning. Examples include the Liteflux LFxx series, and the Pelican 7060.
Some lights are what I would consider semi-regulated. For example, the Fenix Lights like the L0D still do drop in output as the battery voltage drops, but not as severely as in the case of a direct drive light, or "dumb booster". I haven't reverse-engineerd the circuit, but I suspect these are most likely open loop (no feedback), but still with some form of pre-programmed control based on input battery voltage
A third category is a light that is regulated, or semi-regulated to a point, then falls out of regulatoin. An example of this is a light with a buck converter (step-down regulator only), and a single LiIon cell. Whe nthe cell is fresh, the battery voltage is 4.2, and thus stepped down. Howeve,r during the runtime, the battery voltage eventually droips to the p[oint where it drops to match the LED forward voltage. Since the driver is incapable of boosting the voltage to compensate, it simply runs in direct drive thereafter.
In the case of some flashlights, seeing:
"3 hrs regulated, 14 hrs unregulated" would imply the use of primary batteries, and would indicate that the light output is kept constant for 3 hrs, after which the light is direct drive for 14 hrs. It could also mean that you either get 3 hrs regulated or 14 hrs unregulated. Your best bet would be to contact the reseller or manufactuerer for clarification.
My guess is a the first -- there would be no reason to design a light to give the option of running in an "unregulated mode". It woudl be more sensible to simply offer a lower output, but still regulated, mode.