Windows 64-bit has a single calling convention so you can just use extern "C" there and everything will work fine.
Windows 32-bit has multiple calling conventions, cdecl stdcall and fastcall (plus some other less common ones that nobody cares about). "cdecl" is the same as "C". "stdcall" is the same as "system". Most of Windows API uses "stdcall", and various libraries will use either "cdecl" or "stdcall", and you'd have to check carefully to know for sure which one they used.