Or is it its own network.
In a way I guess you're right both ways. It started out it's own network but has since basically been merged into the ed2k network.
So its just one of the clients of edk2000
it uses the same protocol to transfer files as edonkey, the difference is the file indexing, edonkey (the protocol) uses servers to index the connected clients shared files and handle search requests, overnet (the protocol) is a distributed decentralized serverless network, where each node indexes connected nodes shares
emule has it's own distributed hash table network called KAD, a lot like overnet but better and opensource