They're both protocols for arbitrary message sending over the Internet.

Nostr stands for "Notes and Other Stuff Transmitted by Relays".

Messages on Nostr are intended to be "published" meaning they are posted to relays and able to be accessed multiple times by many clients.

I2P stands for "Invisible Internet Project".

Messages on I2P are intended to be "delivered" to a single router much like a payment over LN.

Nostr a new protocol, not very battle tested.

I2P has been around since the early 2000's.

In Nostr, there are clients and relays.

In I2P there are only routers.

Nostr is more focused on censorship resistance. Messages on Nostr are signed, but the messages could also be encrypted and decrypted if published/viewed by clients that implemented encryption. Encryption isn't baked into the protocol.

Messages on I2P are onion routed like Tor or HTLCs on LN. Although, they call it "garlic routing" on I2P.