Basically Zw functions are equivalent of Nt functions except they don't do security checks, so are used inside kernel mode only, to avoid the performance penalty.
You can only call Nt functions from user mode, through ntdll.dll. As Michael pointed out Zw functions are just mnemonics to Nt counterparts in user mode.
@Adriano provided a nice link: http://msdn.microsoft.com/en-us/library/windows/hardware/ff565438(v=vs.85).aspx