Linear bushings run on round shafts and cannot resist rotation; a second shaft or key is needed to prevent the carriage from turning.
Ball splines run in grooves, so one shaft provides both guidance and anti-rotation, and can transmit torque. This saves space and parts in compact axes.
Choose a linear bushing for low-cost, low-precision guidance; choose a ball spline whenever torque, rotation or compact single-shaft design is required.