Image Source : Southern Fabricating Machinery Sales

Wired EDM:  This is a unconventional process, in which there is no direct contact between the tool and workpiece. In this process a moving metallic wire of small diameter is used to cut a work piece. The sparks between the wire and workpiece are used to remove the material. The wire used may be of diameter 0.1 mm, which is made of brass,copper,molybdenum etc. Here the wire acts as a electrode.Applications are medical,aerospace,cutting of gears.

Die sinking EDM:  In this process the electrode and the workpiece are submerged in an insulating liquid. And then power supply is generated,which controls the movement of workpiece and electrical discharges. In this way the sparks are generated in between them.

Die Sinking EDM Wired EDM
In this process the die is used as an electrode which is used for generating sparks. In this process, the wire acts as an electrode which is conductive.
The die is used for cutting any complex shapes.So it is used for both 2D and 3D cutting. The wire cannot cut complex shapes.So it is used only for 2D cutting.
The process begins at any location on the workpiece. The process begins only from the specified position i.e edges 
This is used for drilling,finishing etc. This is used for separating the parts.
Die sinking EDM can produce holes and cavities. Wired EDM is used for cutting.