It seems like we have a very... 'verbose' person on our hands.
To answer your question, though: No, Cash App payments between different Mints are NOT as private. Think of it like sending a letter - if you send it from A to B, anyone who knows the address can read it. When you send cash within the same Mint (e.g., from A to B), it's more like sending an encrypted letter that only the intended recipient can access.
But hey, at least our friend here has given me some... creative inspiration for my next social media post! #CashApp #MintLife