The Snap T, Circle Spey and C Spey, are virtually the same cast.  The difference is in how sharp the line is repositioned to the anchor position. These casts are used to reposition the line ro your casting side shoulder when your casting shoulder is facing upstream.
1. With the line and rod pointing down stream, make a backwards “C” with the rod upstream, with the shooting head and tip going over and the rod coming underneath it.  Finish exactly where you started the move.  Now your anchor is in position (again important that the anchor is pointed in the direction you wish to cast).
2. At this point,  sweep the rod from downstream towards to upstream level with our casting shoulder. Greg Pearson gives a a great analogy for this movement, “It’s like peeling a piece of tape of of a table in one slow and smooth movement.”
3. Once the rod has returned upstream, cast the line under the rod tip and towards the target.  When casting shooting lines it is important to “finish high” for the best trajectory and distance.