Is Swift a general purpose language? I thought it was for iOS and Mac development. I understand it is open source, but so is C#, and I don't see a lot of people using that outside of Windows (I could be wrong though).
I think C# is pretty a pretty common cross-platform language for games due to Unity's support for it. It's not common for other apps, though.
I don't think there's much cross-platform work being done in Swift yet. Give it a little time, though, it's only been open sourced for a few months.
One nice thing about it compared to many other languages is that it can use C APIs with almost no work. There's no need to screw around with annoying FFI systems, you just point the compiler at your C headers and the calls become available in Swift. They may not be very idiomatic Swift, but they're at least no more difficult to use in Swift than they are in C. That means that you don't necessarily need a bunch of Swift libraries to be built before you can start getting stuff done.
If you're looking for stable code with an actual complete, working standard library, it's restricted to iOS and Mac development right now.
Support for other platforms is an area of active development right now, though. The language itself is pretty much already there (for Linux, at least), with an official release for Ubuntu (and it's buildable on other distros), but the supporting frameworks around it are still a work in progress.
It definitely started off for only iOS & Mac. But I believe the larger aim is to have it be general purpose. For example they have binaries for Ubuntu Linux (this will likely encourage server side development).
C# is the native language for the Unity game engine, which is very cross-platform. Now you can use several languages, but I think originally it was C# only.
I don't think there's much cross-platform work being done in Swift yet. Give it a little time, though, it's only been open sourced for a few months.
One nice thing about it compared to many other languages is that it can use C APIs with almost no work. There's no need to screw around with annoying FFI systems, you just point the compiler at your C headers and the calls become available in Swift. They may not be very idiomatic Swift, but they're at least no more difficult to use in Swift than they are in C. That means that you don't necessarily need a bunch of Swift libraries to be built before you can start getting stuff done.