Interfacial sliding speed and contact pressure between the sub-units of particulate soft matter assemblies can vary dramatically across systems and with dynamic conditions. By extension, frictional interactions between particles may play a key role in their assembly, global configuration, collective motion, and bulk material properties. For example, in tightly packed assemblies of microgels - colloidal microspheres made of hydrogel - particle stiffness controls the fragility of the glassy state formed by the particles. The interplay between particle stiffness and shear stress is likely mediated by particle-particle normal forces, highlighting the potential role of hydrogel-hydrogel friction. Here we study friction at a twinned "Gemini" interface between hydrogels. We construct a lubrication curve that spans four orders of magnitude in sliding speed, and find qualitatively different behaviour from traditional lubrication of engineering material surfaces; fundamentally different types of lubrication occur at the hydrogel Gemini interface. We also explore the role played by polymer solubility and hydrogel-hydrogel adhesion in hydrogel friction. We find that polymer network elasticity, mesh size, and single-chain relaxation times can describe friction at the gel-gel interface, including a transition between lubrication regimes with varying sliding speed.