  The importance of the existence of a radiative core in generating a
solar-like magnetic dynamo is still unclear. Analytic models and
magnetohydrodynamic simulations of stars suggest the thin layer between a
star's radiative core and its convective zone can produce shearing that
reproduces key characteristics of a solar-like dynamo. However, recent studies
suggest fully and partially convective stars exhibit very similar
period-activity relations, hinting that dynamos generated by stars with and
without radiative cores hold similar properties. Here, using kinematic ages, we
discover an abrupt change in the stellar spin-down law across the fully
convective boundary. We found that fully convective stars exhibit a higher
angular momentum loss rate, corresponding to a torque that is $\sim$ 2.25 times
higher for a given angular velocity than partially convective stars around the
fully convective boundary. This requires a dipole field strength that is larger
by a factor of $\sim$2.5, a mass loss rate that is $\sim$4.2 times larger, or
some combination of both of those factors. Since stellar-wind torques depend
primarily on large-scale magnetic fields and mass loss rates, both of which
derive from magnetic activity, the observed abrupt change in spin-down law
suggests that the dynamos of partially and fully convective stars may be
fundamentally different
