We apply a recently developed particle-tracking velocimetric (PTV) method along with conventional rheometric measurements to elucidate the nature of one class of nonlinear behavior of entangled polymer solutions under shear. At a fixed degree of chain entanglement, i.e., with the same parent polymer at 10 wt % concentration, we use different liquid media as the solvent to control the upper bound of interfacial wall slip. Contrary to the common perception that these solutions would undergo quiescent relaxation after experiencing a sudden shear strain, we observe macroscopic motions either in the sample interior or at the sample/wall interfaces, corresponding to type A or C behavior, respectively. These macroscopic motions cause the residual stress to decline faster than relaxation due to quiescent molecular diffusion. We illustrate that a continuous range of relaxation behavior can be observed for solutions of the same level of chain entanglement, with one thing in common that the sufficiently strained polymers (with entanglements per chain higher than 10) do not relax the residual stress quiescently upon shear cessation and yield either at the interfaces or in the sample interior due to the retraction force built by the, external strain.