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The signcryption and the authenticated encryption are both the combine of encryption and authentication with three natural composition (i.e., EtS, StE, E&S). I am not sure that if they are the same cryptographic primitive.

If they are the same, why a cryptographic primitive has two different names?

If not, the only difference I personally found is that signcryption is a symmetric version and another is an asymmetric version. But I strongly believe that the difference I found is not true.

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Your finding is correct. From your links;

In cryptography, signcryption is a public-key primitive that simultaneously performs the functions of both digital signature and encryption.

Authenticated encryption (AE) and authenticated encryption with associated data (AEAD) are forms of encryption which simultaneously assure the confidentiality and authenticity of data.

The signing in signcryption is performed with the private key operation. This can provide non-repudation since only the owner of the private key can sign.

The authentication in AE is performed with a shared key between parties. This cannot provide non-repudation since both parties have the key. We can say that the authenticity is mutual.

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