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The Burst and Transient Source Experiment (BATSE) classifies cosmologicalgamma-ray bursts (GRBs) into short (less than 2 s) and long (over 2 s) events,commonly attributed to mergers of compact objects and, respectively, peculiarcore-collapse supernovae. This standard classification has recently beenchallenged by the {\em Swift} discovery of short GRBs showing Extended Emission(SGRBEE) and nearby long GRBs without an accompanying supernova (LGRBN). Bothshow an initial hard pulse, characteristic of SGRBs, followed by a longduration soft tail. We here consider the spectral peak energy($E_{p,i}$)-radiated energy $(E_{iso})$ correlation and the redshiftdistributions to probe the astronomical and physical origin of these differentclasses of GRBs. We consider {\em Swift} events of $15$ SGRBs, $7$ SGRBEEs, 3LGRBNs and 230 LGRBs. The spectral-energy properties of the initial pulse ofboth SGRBEE and LGRBNs are found to coincide with those of SGRBs. A Monte Carlosimulation shows that the redshift distributions of SGRBs, SGRBEE and LGRBNsfall outside the distribution of LGRBs at 4.75$\,\sigma$, 4.67$\,\sigma$ and4.31$\sigma$, respectively. A distinct origin of SGRBEEs with respect to LGRBsis also supported by the elliptical host galaxies of the SGRBEE events 050509Band 050724. This combined evidence supports the hypothesis that SGRBEE andLGRBNs originate in mergers as SGRBs. Moreover, long/soft tail of SGRB andLGRBNs satisfy the same $E_{p,i}-E_{iso}$ Amati-correlation holding for normalLGRBs. This fact points to rapidly rotating black holes as a common long-livedinner engine produced by different astronomical progenitors (mergers andsupernovae).

On the origin of short GRBs with Extended Emission and long GRBs without associated SN