Gyrokinetic tokamak plasmas can exhibit intrinsic toroidal rotation driven by the residual stress. While most studies have attributed the residual stress to the parallel-momentum flux from the turbulent $\boldsymbol{E}\times\boldsymbol{B}$ motion, the parallel-momentum flux from the drift-orbit motion (denoted $\Pi_\parallel^D$) and the $\boldsymbol{E}\times\boldsymbol{B}$-momentum flux from the $\boldsymbol{E}\times\boldsymbol{B}$ motion (denoted $\Pi_{E\times B}$) are often neglected. Here, we use the global total-$f$ gyrokinetic code XGC to study the residual stress in the core and the edge of a DIII-D H-mode plasma. Numerical results show that both $\Pi_\parallel^D$ and $\Pi_{E\times B}$ make up a significant portion of the residual stress. In particular, $\Pi_\parallel^D$ in the core is higher than the collisional neoclassical level in the presence of turbulence, while in the edge it represents an outflux of counter-current momentum even without turbulence. Using a recently developed ``orbit-flux'' formulation, we show that the higher-than-neoclassical-level $\Pi_\parallel^D$ in the core is driven by turbulence, while the outflux of counter-current momentum from the edge is mainly due to collisional ion orbit loss. These results suggest that $\Pi_\parallel^D$ and $\Pi_{E\times B}$ can be important for the study of intrinsic toroidal rotation.
