  Mott-Hubbard and Hund electron correlations have been realized thus far in
separate classes of materials. Here, we show that a single moir\'e homobilayer
encompasses both kinds of physics in a controllable manner. We develop a
microscopic multiband model that we solve by dynamical mean-field theory to
nonperturbatively address the local many-body correlations. We demonstrate how
tuning with twist angle, dielectric screening, and hole density allows us to
switch between Mott-Hubbard and Hund correlated states in a twisted WSe$_2$
bilayer. The underlying mechanism is based on controlling
Coulomb-interaction-driven orbital polarization and the energetics of
concomitant local singlet and triplet spin configurations. From a comparison to
recent experimental transport data, we find signatures of a filling-controlled
transition from a triplet charge-transfer insulator to a Hund-Mott metal. Our
finding establishes twisted transition metal dichalcogenides as a tunable
platform for exotic phases of quantum matter emerging from large local spin
moments.
