Sure, I'll do my best.
The old and deprecated DM spec, defined in NIP-04, leaks metadata to anyone who wants to see it. While the content of the messages are themselves encrypted, the information about who is sending and who is receiving is public for all to see. This on its own can be pretty destructive to privacy.
The latest completed DM spec is defined in NIP-17. It is superior to NIP-04 because it uses better encryption (defined in NIP-44), and it does not leak information about who is sending the DM, only who is receiving. Therefore, anyone who is watching can only see that someone specific received a DM, but they cannot tell who they received it from.
We are hopeful about a new spec that is in the works that will also make it impossible to tell who the intended recipient is, unless you are that intended recipient. It will also make private groups a possibility on Nostr. Keep an eye on what @JeffG posts about WhiteNoise for updates on the progress.
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The NIP detailing how we're using MLS is at worth a read.
White Noise is moving along and we'll hopefully have a beta (that won't be changing anything big enough to nuke all your group chats) in a month or two. For now, feel free to use the alpha and send us feedback!

GitHub
Add NIP-EE: E2EE messaging using MLS by erskingardner · Pull Request #1427 · nostr-protocol/nips
Take 2!
This NIP outlines a way to do secure direct and group messaging on Nostr using the MLS protocol.
Easy to read
GitHub
Releases · marmot-protocol/whitenoise-rs
The Rust brain for the White Noise app. Contribute to marmot-protocol/whitenoise-rs development by creating an account on GitHub.
Excellent recap! Thank you for taking the time.