The basic SPICE calculating software is done by a US university and is paid for by the US government. Commercial companies combine their unique interface with this code to make their product. PSpice is a very user friendly product with some limitations caused by its automatically doing things that are good most but not all of the time. HSpice has a more complex interface and much more user selectable settings. It has the best performance possibilities with a skilled user. Many other companies add RF type synthesis abilities.
There are many versions of spice out there. hspice is popular because it provides better model parameters before. But now most of the simulator are based upon BSIM. Basicall, it is the sim speed that differentiates the different versions of spice nowadays.
What make each Spice different? It would be its features and algorithm used to find out the solution. Hspice is successful in this field becuase their engineers work out so much in developing both circuit soluble equation and transistor modeling.