- Regulated lights have circuitry between the batteries and the led to control the current going to the led. This allows the torch to have a pretty much constant output level even as the batteries are being used up. When the batteries are flat or close to flat, a regulated light will suddenly go from full brightness to pretty dim very quickly. An unregulated light will start out bright and start fading immediately as the batteries are used - over time the light will fade away to nothing. Unregulated lights are often advertised with ridiculous battery life - because they count all the time when the light is dim, which will be most of the time
Some unregulated lights (like the x21 I think) can't handle NiMH rechargeables because the NiMH will hold up a higher voltage over a longer time and therefore cause heat issues, whereas alkalines voltage will rapidly drop off, so while with alkalines it will be brighter than NiMH for a couple of minutes or so, after that they will be much dimmer. With a regulated light generally you wouldn't see any difference between alkalines and nimh.
Some lumen ratings are pretty trustworthy - look for ansi lumens, or at least OTF (out the front) lumens being specified. If you don't see those, in most cases it will be a pretty wild claim.
800 lumens is 4 times as much light coming out the torch compared to 200 lumens. But it won't look 4 times brighter to your eyes because our eyes don't see brightness linearly. It might look twice as bright or thereabouts. Lumens are the total amount of light, but do not tell you how tightly focused that light is so it doesn't tell you how far the torch will throw the light, for that look at lux.