A bit of a quick answer here so please ask further if you still have difficulty understanding.
Looking at the pics in your links the difference in size is down to one lens having a built in focus motor ( AFS ) and the other not having it but being driven by a screw drive from the camera body.
The first thing to understand about lenses is ' focal length ' this equates to angle of view. Look through your camera and zoom from 18 to 55 and you will see that at the 18mm end the view is considerably wider than at 55mm. Check out this link to see the effect over a wider range of ' focal lengths '.
http://www.tamroneurope.com/flc.htm
Lens size is down to several factors.
1) Built in focus motor ( AFS ) will give a greater lens body diameter than a manual focus or screw driven A/F lens.
2) The size of the front element is down to the size of the largest aperture. If a lens can open up to f2.8 then the front element glass will be of a larger diameter than a similar lens where f5.6 is the maximum aperture.
3) Focal length of the lens itself. As the focal length increases say from 55 to 300mm so the length of the lens grows.
Cost ..... well that is purely down to the quality of the optics. Lenses that have been well corrected optically and give high resolution ( ability to capture fine detail ) cost a lot more than those of lesser ability. Also zoom lenses that cover a huge range say 18-200mm are costlier to design and make than a lens covering 18-55mm. Now add a focus motor and possibly a VR unit and the cost goes up again.
Don