The laminar-turbulent transition of spherical Couette flow between two independently rotating concentric spheres for the gap ratio 0.14 where the Taylor instability occurs for the fixed outer sphere has been investigated by simultaneous spectral and flow-visualization measurements. Rotation frequencies (phase velocities) of periodic disturbances do not so much depend on the ratio of the outer-to the inner-sphere rotating Reynolds number if they are non-dimensionalized by the mean rotation frequency of both spheres. Traveling azimuthal waves on only an inflow boundary of toroidal Taylor-Gortler (TG) vortices and herring-bone waves appear for the case of co-rotating spheres, while spiral vortices and twists in toroidal TG vortices appear for the case of counter-rotating spheres. Flow regimes and their occurrence-regions in the plane of the inner- and outer-sphere rotating Reynolds numbers differ depending on the Reynolds-number history.