Shofars are usually made from rams horns. Every horn will be different both in terms of size and structure. That means they will all have different pitches and harmonics.
They were originally war horns. Most of the calls are based on those roots. In essence though, they are no different from any other horn. I think they are very similar to dijeridus in terms of how they came to exist. They also play fairly similarly, except for the size. Kind of like a trumpet vs a tuba.