Yes, minibits wallet address works for both protocol. Nostr identity allows to deliver ecash to the wallet over nostr encrypted messages.

It is not assumed to become your public nostr address - private key is never exposed and can't be imported to any nostr client.

So normal usage is that you add your minibits address to your existing public nostr profile to be able to receive zaps or other payments.

When you send ecash to someone else with nostr address, you can skip lightning and send it as an ecash token - you can keep nostr profiles in contacts.