What is the name of the boundary between Earth’s sunlit and dark sides?

The terminator is the boundary between Earth’s sunlit and dark sides.

Earth’s terminator is the moving line separating day from night. It is not a fixed geographic feature: Earth’s rotation makes it sweep around the planet each day, while the planet’s axial tilt changes its position and shape through the year. Seen from space, the boundary can appear curved because Earth is spherical, although local terrain and clouds make the visible line irregular.

At an equinox, the terminator is approximately aligned with Earth’s axis and passes close to both poles. Around the solstices, Earth’s tilt makes the boundary reach farthest north or south, producing the longest and shortest daylight periods in different hemispheres. Twilight means the surface may still be partly illuminated before sunrise or after sunset, so the visible transition is broader than the ideal geometric boundary. The same term is used for other illuminated bodies, including the Moon.