That, and the terms themselves tend to invoke clues about the meaning.
Privacy implies there is an identity, but it is kept hidden.
Anonymity implies there is no identity established so there is nothing to hide.
We don't see much of the latter since most web services require an email to sign up, at minimum, which still leaves discoverable bread crumbs. The web services that require you to give up nothing to use them are far less popular, so I guess I can see why people might conflate the two.
