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There is the natural use for either transmission over an insecure network or for storage on an insecure media.
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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
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This is effective authentication but requires as many secrets as pairs of people who need to communicate.
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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.
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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.
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