A “full” nostr client refers to one which is fully interoperable with other nostr apps — content created and relayed in one can be seen in another, as long as there’s a shared relay. My understanding of cornychat is that it incorporates some nostr features but functions adjacent to the nostr protocol, rather than implicitly dependent on it.
I could be wrong and would appreciate clarification if I’m missing anything. Cornychat is great, nonetheless, but I believe there’s information that doesn’t get sent as nostr events to relays.