Proxies can be setup to sign specific or all (any) transactions on behalf of an account. You could say that the account is proxied, if it has a proxy.
There is a provision to create a keyless account which can be fully functional only when there is at least one proxy with any permissions to sign transactions on its behalf. This account (without a private key) is a proxied account. It is also not anonymous, as it is assigned a public key and can be traced on the blockchain.
Hence, it is neither Anonymous nor a proxy. Then why is it called an Anonymous Proxy?