We report a structural polymorphism of the S-DNA when a canonical B-DNA is stretched under different pulling protocols and provide a fundamental molecular understanding of the DNA stretching mechanism. Extensive all atom molecular dynamics simulations reveal a clear formation of S-DNA when the B-DNA is stretched along the 3' directions of the opposite strands (OS3) and is characterized by the changes in the number of H-bonds, entropy, and free energy. Stretching along the 5' directions of the opposite strands (OS5) leads to force induced melting form of the DNA. Interestingly, stretching along the opposite ends of the same strand leads to a coexistence of both the S- and melted M-DNA structures. We also do the structural characterization of the S-DNA by calculating various helical parameters. We find that the S-DNA has a twist of ∼10° which corresponds to a helical repeat length of ∼36 base pairs in close agreement with the previous experimental results. Moreover, we find that the free energy barrier between the canonical and overstretched states of DNA is higher for the same termini pulling protocol in comparison to all other protocols considered in this work. Overall, our observations not only reconcile with the available experimental results qualitatively but also enhance the understanding of different overstretched DNA structures.