So radar works in the sense that its a wave of microwave energy flowing through the air, bouncing off objects as it hits them and dispersing and loosing energy the further it goes. Typically a cop will have constant on radar, normally within the K and Ka bandwidth, which is a certan hz signal. Most falses will come in X and K band wavelengths as many radar devices (door openers) now use them. Typically their range is one to two blocks. A directed police Ka radar beam has a very tight wavelength and will carry much further and can deflect off many objects. If you pick up a very strong Ka signal, more than likely thats the police. Some highway patrol use instant on or POP radar, which is between K and Ka (more likely Ka) band and will have a very short but strong signal, generally detectable by a good radar at 1/4 to 1/2 mile. How this works is the officer will see an approaching vehicle, hit a button on his remote and his radar will make a very short burst, less than a second, to make a semi accurate reading (though this is debatable). The best defence to Pop or instant on is to let one or two cars get ahead of you, bout a half mile and listen for a chirp or two in those specific bands. You will generally know when its a cop because of the high signal strength and short burst time. So long story short, microwave radar carries much further, but needs to be very close 500 - 1000 ft in most cases to get a good reading. Of course on a perfect day on a 2 mile line of sight straight away it is possible to get a clocked speed on a vehicle. Laser is very different. Laser is light. As the distance increase, the beam grows in diameter. The light will travel at ofcourse light speefld, reflect off a shiny surface and back to the radar device, producing a speed reading in very very little time. Normally the moment you get a laser hit on your detector its to late, they've got your speed. Generally laser works at 500 to 1500 ft, always direct line of sight, and can single out individual vehicles and even record a short video to further assist in court. Advantage, laser must be stationary and cannot be used in a moving police vehicle. Some radars are sensitive enough to pick up stray laser waves boumcing off the windshield of the vehicle infront of you and may save you from a ticket if you are speeding, but laser traps are wicked because they can be much more difficult to spot.
Hope that explains it, sorry for droning on