Uses of Secret Key Cryptography
There is the natural use for either transmission over an insecure network or for storage on an insecure media.
Strong Authentication implies that one can prove knowledge of a secret (key) without revealing the key and in particular without sending key between two individuals
This is effective authentication but requires as many secrets as pairs of people who need to communicate.
Public key version will only require one key for each individual wishing to be authenticated with anybody else and so is more practical for widespread deployment. N keys and not N2 as for secret key authentication.
Secret key authentication is however faster and much easier to implement for any sets of sites that wish to establish authenticated communication with a shared secret.