The primary difference between LN and Monero for privacy as a regular user is that the recipient node is always public on LN. Both sender and receiver are anonymous on Monero. So are all wallets and balances. The only thing the blockchain ever shows is "anon sent an unknown amount of money to another anon."

There's a lot of complex details regarding the design of the underlying cryptography as well, such as rings and decoy transactions. This makes unmasking transactions much more difficult because you don't even know what to target.

The nostr:npub1tr4dstaptd2sp98h7hlysp8qle6mw7wmauhfkgz3rmxdd8ndprusnw2y5g link on Monero that's already been posted further down is a great resource to learn more.