Both! Your staff will use the Windows interface for VSys One, or web for VSys Anywhere. Volunteers can use VSys Kiosk (touch screen), VSys Live Kiosk, VSys Web or VSys Live interfaces to sign in and out, update their information, see their assignments, etc. (VSys Web is entirely optional, but included with your license.)
If you use the hosted version of VSys One, you get the very same programs but without the need for your own servers or to install anything at all, and you can access VSys from anywhere in the world.
For self-hosted VSys, where the software runs in your IT department and is 100% under your own control, your IT department can make VSys available to you anywhere in the world using a VPN and Citrix, Terminal Services, or Remote Desktop systems, and do so securely.
If you're using the hosted version of VSys One, VSys remains a Windows application but it's one that you can access from anywhere and from most types of machines.