Are processors designed using different technologies?
The whole processor is built with the same technology. This is determined by the mask(s) and optics to project them on each die on a wafer (a process called "stepping"). Smaller feature sizes allow more components to be packed on a die, lower power consumption and higher speed. It's no use spending a small fortune (they do cost a small fortune) on a mask and then not use its possibilities.

To be clear: yes, the same 28 nm will be used for one step for the complete die surface, but no, not all components will be the same size. It's just that the 28 nm mask won't be swapped for a 65 nm mask for part of the die.

edit
There are indeed larger areas on a die which don't require the 28 nm small size. Typical is the solder ball pads for a flip chip:  

  

Notice the scale: these pads are 1000 times larger than the finest structures on the die. Here a less fine mask may be used, but again, if the process step would also require the 28 nm then the same mask will be used for both. It's not because the pads are gigantic that they don't have to be positioned precisely, and that's less error-prone if you don't have to switch masks.