Element on Nostr: In a non-E2EE application, Bob can trust the server that the message is from Alice ...

In a non-E2EE application, Bob can trust the server that the message is from Alice (as Alice is authenticated). In E2EE, Bob needs to check (cryptographically verify) that the keys of Alice’s new device used for message encryption, are cryptographically linked to Alice’s identity.

This is a slightly simplified & compressed summary for those who are more tech savvy.

For a non-technical user the simplified summary is that other users can always be sure that this device belongs to you.