Difference between Tag and Signature Is there a technical difference between tag such as tag generated by authenticated encryption, and signature such as the signature generated by a functional signature scheme or homomorphic signature scheme.
The authentication tag is the output parameter, like in AES-GCM, which is generated by the symmetric key to authenticate the message. 

$$(c,tag) = \operatorname{AES-GCM-Enc}(key,m,IV,AD)$$

Where $A$ is the Associated Data. The tag is verified by the same key, IV, and AD.

$$(\{T,F\},m?) = \operatorname{AES-GCM-Dec}(key,c,IV,tag,AD)$$ The tag verification must be performed before using the plaintext. 

A signature, digital signature, is created by using the asymmetric encryption mechanisms using the private key. Such as DSA, ECDSA, EdDSA, or RSA signatures. The digital signature can only be created by the private key owner, and it can be verified by anyone who knows your public key. The secure hashing mechanism is an integral part of secure signatures not due to signing small messages.

$$\text{signature} = \operatorname{Sign}(k_{prv}, m)$$

$$ \{T,F\}\stackrel{?}{=} \operatorname{Verify}(\text{signature},k_{pub},m)$$

So the distinction is; the tag is generated by the symmetric key and the signature is generated by private-key.