A dynamical analogy supported by five scale-free statistics (the Gutenberg-Richter distribution of event sizes, the distribution of interevent intervals, the Omori and inverse Omori laws, and the conditional waiting time until the next event) is shown to exist between two classes of seizures ("focal" in humans and generalized in animals) and earthquakes. Increments in excitatory interneuronal coupling in animals expose the system's dependence on this parameter and its dynamical transmutability: moderate increases lead to power-law behavior of seizure energy and interevent times, while marked ones to scale-free (power-law) coextensive with characteristic scales and events. The coextensivity of power law and characteristic size regimes is predicted by models of coupled heterogeneous threshold oscillators of relaxation and underscores the role of coupling strength in shaping the dynamics of these systems.