We experimentally study the optical- and terahertz-induced rotational dynamics of asymmetric molecules in the gas phase. Terahertz and optical fields are identified as two distinct control handles over asymmetric molecules, as they couple to the rotational degrees of freedom via the molecular dipole and polarizability selectively. The distinction between those two rotational handles is highlighted by different types of quantum revivals observed in long-duration (>100 ps) field-free rotational evolution. The experimental results are in excellent agreement with random phase wave function (RPWF) simulations [Phys. Rev. A 91, 063420 (2015)] and provide verification of the RPWF as an efficient method for calculating asymmetric molecular dynamics at ambient temperatures, where exact calculation methods are practically not feasible. Our observations and analysis pave the way for orchestrated excitations by both optical and terahertz fields as complementary rotational handles that enable a plethora of new possibilities in three-dimensional rotational control of asymmetric molecules.