Slant stacks are closely related to Snell waves. But there is more to it than that. Three different types of gathers (CSP, CGP, and CMP) can be slant stacked, and the meaning is different in each case.
A Snell wave can be synthesized by slant stacking ordinary reflection data.
Snell waves are described by wave-propagation theory.
You can expect to be able to write a wave equation that really describes the
Snell wave despite complexities of lateral velocity variation,
multiple reflections, shear waves, or all these complications at once.
Contrast this to a CDP stack where downward continuation is already
an approximation even when velocity is constant.
Of course we can always return to data analysis in shot-geophone space.
But the slant stack is a stack, and that means there is already
some noise reduction and data compression.