I believe that 'shaping' should differentiated from 'splitting' stone in that it involves breaking a stone across its narrower thickness. It can also involve breaking a stone to create a rough face and/or obviously giving it some sort purposeful shape.
Splitting on the other hand involves opening a stone up along its grain or sometimes across, (sometimes using feather and wedges or a 'tracer') but usually involves bigger pieces than ones we will be shaping and splitting generally is done more at the rough beginning stages of a project.
I rarely 'split' stones unless perhaps I come across a stone that is layered and has a fault or a fissure where it seems like it would be easy to chisel open to separate it into two matching halves. The twin stones with newly revealed surfaces are sometimes called 'shiners'. Shiners are rarely used structurally, that is, with their faces showing out in a dry stone wall because they are generally too thin and the bulk of the stones can't be embedded into the wall deep enough.
Shaping is more likely to be what we do to the stones in normal dry stone walling. It is what you see going on in this photo above. The stone is too long and the wrong 'shape' to go into the abutment we are making for the bridge. If we need to make a new face on a stone we can cut (shape) it this way too.
To use the stone we have to shape it with a chisel and hammer. Ironically the chisel is a two inch 'splitter'. It has a carbide tip blade and a one inch shank (which makes it easy to grip and sends the blow of the hammer down with more force into the stone)
Granted, a single hammer known as a walling hammer could be used inserted to do this kind of shaping but it involves more of a gradual chopping away at one side of the stone to get the stone to the right size. I prefer to just cut across the stone the way you see it is being done here along the line scratched on the stone in the photo above.
I use a three pound lump hammer holding the splitter firmly gripping it nearer the pointed end of the chisel. The chisel blade has to be positioned exactly along the line I want it to break. It needs to touch the stone's surface in at least two points so that the chisel isn't resting on a high point which would only allow the force of the blow to one small (directionless) point. With the chisel blade touching the surface in at least two places on the line, the force of the blow is spread/connected? along the length of the chisel width at least, and so sends the message/energy of the impact along the proper orientation.
Enough hard whacks will eventually tell the stone where it should think about breaking. If it the stone I am shaping is fairly flat and big enough I sometimes put a straight piece of metal ( T-bar or rail or even a pry bar) under it parallel to my line so that the blow from the hammer is sent directly down below along the line where the stone is resting. Sometimes if it is taking a while and I want to make sure it breaks in the right place I turn the stone over and chisel the other side too.
Eventually the stone will break and usually if it is the right kind of stone (granite sandstone and limestone are good) it will produce a clean flat straight break which can often be used as a 'face'.