This might help:
Discussion
Just sent myself a few sats from what I had left in WoS to test, it took longer than I expected, but I guess the mint operation takes a few moments - so now I've got that, I can give that to anyone and there's no record?
If you send it to a lightning address, you will incur a tiny fee, but free if you send it to another cashu address.
If you send it to another cashu address of a different mint, these cashus will get destroyed by the receiving mint and then reissued as new and forwarded to the receiving address.
Between mints and users and between mints themselves, it's totally private. When sending to lightning, I'm not too sure.
Someone please correct me if I'm wrong.