Does an anonymous signature hide the sender's identity from the receiver, or simply just hide the sender's identity from an eavesdropper or third party?
It is perhaps more complicated.
Signer anonymity for anonymous signatures means anyone who has the signature but not the message (or does not know enough about the message) cannot reveal the identity of the signer.
Thus it really depends on, in your model, what the receiver or eavesdropper knows. For example, if one sends the signature and the message (in plaintext) together, then even the eavesdropper can know the signer's identity. For receivers, often they are supposed to verify a signature, so they know the identity of the signer. However, if your receivers are not verifiers (e.g. they just receive and store the signatures), then they may not need to know the messages, and if the messages are hidden from them, then they don't know the identity of the signer.