The Server.app DNS function is definitely a real full-blown 100% genuine DNS server. It is actually a GUI front-end to the standard BIND aka Named DNS server software that is the most widely used DNS server software in the world.
It is admittedly most commonly used to only provide internal DNS features for your LAN but nothing at all prevents you from using it for external i.e. Internet usage.
See http://krypted.com/mac-security/setup-the-dns-service-in-os-x-mavericks-server/
The only router related DNS function I can think of in Server.app that you might be getting confused with is that Server.app can in some circumstances configure the settings of Apple's AirPort Extreme base station. This is however a separate function and not the something as the full-blown DNS feature as per the article above.