If you want to express the speed of a moving object with respect to its surroundings then the best way is to capture motion blur in your photograph. Capturing motion blur requires a lot of proficiency and experience, hence it is an extremely tuff discipline of photography for novice photographers.

Still to give a brief insight into capturing motion blur, it s necessary to know that there are two kinds of motion blur that you can capture in your photograph.
The first kind of blur is the kind achieved in the photograph on your left. In this photograph the horse which is at high sped is in focus whereas the surroundings are blurred. This is called the Motion Blur of the background and requires the technique of Panning.

To achieve a photograph like this you need to keep the following tips in mind-

1. Focus your camera on the moving object; keep a deep depth of focus as the object is constantly moving and the focus likely to change.
2. Keep the camera on a high shutter speed and place it on a tripod to avoid any jerks
3. To blur the surroundings, pan the camera along with the moving object and click while panning, do not stop and click because then the effect will be reversed.

The second kind of motion blur is the one in which the object in motion is blurred and the still objects or the surroundings are in focus, as you can see in the picture on your left. To achieve such results you need to do contrary to what you did in the first case. Now you need to keep low shutter speed, which is usually lower than 1/60th of a second and keep the camera absolutely static and stable.
Capturing motion blur is an art and you need to choose which kind of motion blur amongst the two will add that extra edge to your photograph.