Lets fill out the second statement with as much context and nuance.

"

Every lightning transaction is a trade using a sequence of unconfirmed transactions that can be settled by either party.

Every transaction in e-cash is a record in a database." The data that is stored by the servers is unrelateable to the data the client has. UNLESS, a client generated secret is shared with the server. The client remains in control of the blinding mechanism. The client can selectively reveal itself. This is the privacy of blinded signatures as used by ecash. "