Let's discuss what each of the terms mentioned in your question means.

• Fill Flash: When there is enough overall light in the scene to take a picture, but there are shadows that need to be smoothed out, fill flash can be used to lighten the shadows. Even outdoors on a sunny day, if the sun is high overhead or behind your subject you can use fill flash to even out the light. The camera computes the shutter speed and/or aperture needed for the overall scene, then adds enough flash to fill in the shadows. You may need to adjust Flash Exposure Compensation to get the look you want. The power needed can be very little to full power, depending on the shooting conditions.

• Slow Sync Flash (a/k/a Slow Shutter Flash): This is the counterpart of fill flash. When there is not enough light to take a good exposure but you want many areas of the scene to be lit. The camera computes the shutter speed needed to properly expose the background, the flash fires with just enough power to properly illuminate your subject. Shutter speed will generally be slow enough that the camera will need to be supported in some way to prevent blur caused by camera movement. The amount of power needed will vary, depending on the scene.

• High Speed Sync: Each camera with a mechanical shutter has a speed that is the fastest it is capable to sync with a flash. It is usually around 1/200 to 1/250 sec, but can be much faster or slower depending on the camera. At speeds faster than this the second curtain of the shutter begins to close before the first curtain is completely open. The sensor (or film) is not being exposed all at the same time, but instead is being exposed from top to bottom (or side to side for most older film cameras) by the opening between the two curtains. The faster the shutter speed, the narrower the gap between the first and second curtain. Since an electric flash strobes at a very short duration, only the fraction of the sensor that is behind the slit between the two curtains will be exposed to the light from the flash, and the top and bottom of the frame will have dark bars across them. The solution when flash is needed at a high shutter speed is for the flash to fire a series of bursts while the curtains move across the sensor. This means the flash must fire several times in very quick succession. To have enough power for that many pulses of light, each one must be weaker than a single, high powered burst. Each pulse is dimmer, but because the flash is pulsing many times, the total power used is relatively high in most cases.

• Second (Rear) Curtain Sync: Normally the flash fires as soon as the first curtain is completely open. The camera then waits until the set shutter speed has almost elapsed and then begins closing the second curtain. With Rear Curtain Sync, the flash waits and fires just before the second curtain begins to close. The effect this has on moving objects is to make the place they are at the end of the exposure their brightest spot in the frame. The classic example is of a car traveling forward at night. With normal first curtain sync, the flash would fire early in the exposure and the trails of the headlights would extend in front of the car. Using second curtain sync, the flash would fire almost at the end of the exposure and the car would be seen with the light trails behind it. Second Curtain Sync is most effective when used in conjunction with Slow Sync. The amount of power used varies according to the scene.

In each case described above the amount of power used by the flash is determined by how much light the camera needs to properly expose the scene. Any of them might need more or less power depending on the scene.