LND Rest is a pretty standard way for you to connect your LND node to a wallet app, such as Zeus. However, for node implementations like Start9 and Umbrel, this has to be done over Tor, so it can be quite slow and unreliable to connect.
LND Connect is a way to connect Lightning Terminal running on your node to to Zeus, if I remember right. Lightning Terminal can allow you to set up separate wallets that all use your node's liquidity. It is also much faster and more reliable than LND Rest, because you don't have to connect via Tor.
Embedded LND is just Zeus' node-on-your-phone implementation. It doesn't connect to a separate Lightning node, but rather requires you to manage liquidity in Lightning channels within Zeus. To account for the fact that your phone will often be offline, Zeus uses hodl invoices to hold your received funds for you until you reconnect. I believe they have also implemented a way to use eCash until you build up enough of a balance to justify opening a channel, too, but I haven't had a chance to play with that yet.
Nostr Wallet Connect is a way to connect any compatible wallet to Zeus, whether running on your own node at home, held by a custodian, or even a Nostr wallet that uses eCash stored on relays. Nostr Wallet Connect uses a Nostr relay between the host wallet and Zeus to send encrypted transaction and balance information back and forth. It works quite well, so long as the relay is online. As for where you get the connection string, that is going to differ based on the wallet you are wanting to connect to Zeus.
