Zeroconf (Zero Configuration Networking) is the standards body name. mDNS is one of 3 components that Zeroconf uses, the other two being local link addressing and DNS service discovery.

jMDNS works fine on Android but it is a 3rd party dependency you have to add and it is slow to start up.

Android 4.1 started shipping their own native Zeroconf implementation (Network Service Discovery) which kind of works, but is buggy as hell.

Yeah, kind of. Now that they've rolled some of it into the OS things are better, but in the bad days before 4.0 you'd get devices hard wired to discard any broadcast or multicast packets while the screen was off and so on. Manufacturers had a distinct tendency to mess with anything not explicitly used in the OS.

Google aren't helped when people like Samsung decide to redefine the bump to file transfer to mean NFC to initiate WiFi Direct, not what everyone else had deployed which was Bluetooth, and without the fallback position of making that work. That's the curious thing with Android, they did in many ways engage in the wider world hoping for a bit more wider co-operation (at least within the OHA), but you'd be hard pressed to find an area of the OS anyone other than Google had a positive impact on, but there is plenty of the reverse going on.