It's all in the different types of refrigerants.
A normal single stage uses a refrigerant which will consense at an easily reachable temperature and pressure. First stage refrigerants are limited in that they must condense at room temperature, and at a pressure and flow rate that a regular compressor can keep up with (while keeping the low side pressure low enough to give good evaporation temps). This limits the refrigerant to things like R290, R22, R404a etc. They can all be consensed by a single stage unit, but don't have the extreme evaporation temperatures of other refrigerants.
A cascase is just 2 (or more) single stage units, tied together. The first stage is just like a normal single stage, but it's evaporator cools the condensor of the sencond stage rather than the cpu, gpu etc. This means that the refrigerant of the second stage doesn't have to condense at room temperature, it has to condense at the evap temp of the first stage (say -40 or so). This allows you to run different refrigerants in the second stage which have a much lower evaporation temperature.