Hi Charles,

Exactly. The Earth is covered by a scattering medium (the atmosphere). When the Sun sets, its light is scattered and refracted by our atmosphere which gives us our twilight glow.

A sunset on the Moon is much different. As soon as the Sun is below the horizon, you are in darkness, except for the star light (and Earthshine). It would be somewhat like a light switch: very sudden. The temperature would also drop quite suddenly too!

You can see this effect during occultations. The star does not slowly dim, but suddenly winks out. However, since the Sun has a much larger apparent angular size than a distant star, it does take more time to set.