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?
let's create an "anonymous"(keyless) account and "proxy" it(still not the best name for the action), but then it probably started being used as the name of the kind of account. As you've seen in the linked issue people agree is not the best name and should probably be changed. I guess it's just missing someone putting the work to actually change it