Most likely you haven’t got a quick reply because it is explained in the documentation.
However, to help you a bunch:
Zeroshell is an appliance – a set of applications and custom tools built on top of the underlying Linux operating system.
It’s function is to turn any simple PC into an effective network router with many advanced features configurable via a web browser. This is why the name ‘Zero Shell’ – you do not have to use the Linux shell to configure the normal features.
As for which ‘version’ of Linux – you will have to read the documentation to get the full idea of that. It runs on Linux but not any of the major distributions that most people would be able to name.