A Unified Picture of Short and Long Gamma-ray Bursts from Compact Binary Mergers, Gottlieb et al. (2023) The recent detections of the ~10 s long gamma-ray bursts (GRBs) 211211A and 230307A followed by softer temporally extended emission (EE) and kilonovae, point to a new GRB class. Using state-of-the-art first-principles simulations, we introduce a unifying theoretical framework that connects binary neutron star (BNS) and black hole-NS (BH-NS) merger populations with the fundamental physics governing compact-binary GRBs (cbGRBs). For binaries with large total masses Mtot>2.8 Msun, the compact remnant created by the merger promptly collapses into a BH, surrounded by an accretion disk. The duration of the magnetically arrested disk (MAD) phase sets the duration of the roughly constant power cbGRB and could be influenced by the disk mass, Md: long cbGRBs such as 211211A are produced by massive disks Md>0.1 Msun, which form for large binary mass ratio q>1.2 in BNS or q<3 in BH-NS mergers. Once the disk becomes MAD, the jet power drops with the mass accretion rate as Mdot~1/t^2, establishing the EE decay. Two scenarios are plausible for short cbGRBs. They can be powered by BHs with less massive disks, which form for other q values. Alternatively, for binaries with Mtot<2.8 Msun, mergers should go through a hypermassive NS (HMNS) phase, as inferred for GW170817. Magnetized outflows from such HMNSs, which typically live for < 1 second, offer an alternative progenitor for short cbGRBs. The first scenario is challenged by the bimodal distribution of GRB durations and the fact that the Galactic BNS population peaks at sufficiently low masses that most mergers should go through a HMNS phase. HMNS-powered jets also more readily account for other light curve features, from precursor flares to EE characteristics.