The post office knows who I am, my address, and who sends mail to me. They even know who I send mail to, if I write my return sender details on the envelope. I am not anonymous.
But, if the person we use ciphers to encrypt our letters, and only the two of us can decrypt and read them, our communications can indeed be considered private.
There’s a fundamental difference.
Edit: to answer your crude (but funny) example, I have no expectation of anonymity when I walk into my toilet at home or the toilets at work. The very fact that I, as a man, walk into a stall rather than stand at the urinal, gives any of my colleagues washing their hands at the basin the reasonable confidence of knowing I am taking a shit.
The size of the shit, the faces I make, and the nature of the resulting product, however, are not know to anyone else except me. That’s the difference.