The resonant column test excites the specimen and finds the frequency at which it resonates, from which the shear wave velocity and modulus follow.
The torsional simple shear test applies a controlled torsional load and reads the response directly, which gives modulus and damping from the loop rather than from a frequency.
RC works at very small strains, TSS reaches larger ones. Running both on one specimen is how a stiffness degradation curve is built without changing samples, which is the reason the two are combined in a single unit.