What is the difference between Splitchain and Zucoin?

Zucoin is the native, base token on the Splitchain network.

Splitchain is the layer 1 network, primarily used to ensure transaction proofs from peers are reliably available to other peers.

Doing a transfer in the Zucoin wallet app creates transaction proofs, the results of which are submitted to the Splitchain network, so they can be cached and reliably discovered by other peers.

The Zucoin wallet app does a lot of the heavy lifting and processing gruntwork, including finding transactions on the network, then submitting the processed transactions back to the caching nodes on the Splitchain network.