With R on and the throttle near the speed of light, three things appear on screen: stars bunch into the forward direction (aberration), the forward view brightens while the rear dims (relativistic headlight), and stars color-shift — blue ahead, red behind, eventually shifting out of the visible spectrum entirely (Doppler).
The throttle shows your target rest-frame speed; the SPEED readout shows measured speed in units of c. In classical mode they match. In relativistic mode the measured speed caps at 1c (matter can't exceed light speed), but adding throttle past that keeps increasing γ — the time-dilation factor shown in the HUD. γ = 2 means time on board ticks half as fast as outside; γ = 10, one-tenth as fast.
Star catalog data from the HYG Database v3.8 by David Nash, licensed under CC BY-SA 2.5.