There are main types of brake controller: proportional and time-based.
Proportional brake controllers are inertia-based. There is an inertia sensor in the controller: the harder you brake the two vehicle the more the sensor "feels" it and the harder it applies the brakes. There is also usually a gain or "boost" setting that adjusts how sensitive it is to the feeling of deceleration, as well as a maximum brake setting. The controller does not apply the brakes unless the brake pedal has been depressed (usually wired to the switch that activates the brake lights.
Time-based controllers do not sense how hard you are braking. They just sense that the brake pedal has been depressed (again, triggered by the switch that turns on the brake lights). There is sometimes a delay before the trailer brakes are activated (on some controllers, the delay is adjustable), then the trailer brakes are activated, starting out low and ramping up the longer the brake pedal is depressed. Most controllers have some means of adjusting how quickly the braking force ramps up, and setting a limit for the max braking force. If the vehicle is standing still, the controller will not sense any decelleration and will not apply the trailer brakes. (It's possible that some controllers may have some other circuitry which activates the trailer brakes if the pedal has been depressed long enough: such as to help hold the vehicle while sitting at a stop light. I've never really thought to check on mine.)
Time based controllers a usually less expensive, since the electronics are simpler (no need to sense deceleration rates - a timer circuit is simple). Proportional controllers are generally considered superior technology for on-road towing: the harder you hit the town vehicles brakes, the harder the controller applies the trailer brakes. Time based controllers are often preferred by the off-road crowd: it seems the inertial sensor can sometimes get "confused" by bouncing around off road, resulting in widely varying application of the brakes in uneven terrain. A time based controller works the same regardless of terrain variations. For less demanding towing operations on the road a time based controller works fine.
There are also dual-mode controllers which allow you to switch between the two modes. I put one of these on my old Dodge M37 woods truck. Since it's an antique truck without a lot of the modern safety features, I wanted the best brake controller for on-road situations. However, I also use it in the woods, so the ability to switch to a time based brake controller was helpful in that situation.
