Just like the title says. Is there one single SPICE back-end that's the same for different versions of SPICE, or are the different versions performing different simulations?
The general approach to SPICE simulation is more or less the same for different SPICE simulators...the fundamental laws of circuit analysis haven't changed. What will vary from simulator to simulator and across versions of the same simulator are the techniques used to do numerical integration, achieve convergence, and avoid round-off errors. For elements like transistors there are a variety of models (sets of equations) that can be used, and you may find a variety of model parameters (the coefficients for the equations) for a given part number.
I'm not sure that either of the choices you offer in your question are quite right. It's not clear what you mean by "back-end", "the same", or "different simulations".