Genesis 1:18

and to minister by day and by night, to distinguish between the light of the day and the darkness of the night. And the Lord beheld that it was good.

"and to rule" - the day of the Torah is from the hour that the sun rises until its setting, and the night is from the time of seeing the stars, and they were correct who said: at the word of three witnesses. Know, that the time that the sun become darkened is evening, [continuing] until one and a third hours, when a semblance of light can be seen in the clouds, and likewise morning - light before the [actual] shining of the sun. With the emergence of the light of the sun in the day and the light of the moon at night, [people] will distinguish between light and darkness.

AND TO RULE OVER THE DAY AND OVER THE NIGHT. The matter of rulership is a different matter from the function of light which He mentioned, since it includes that which He stated at first, And they shall be for signs, and seasons. Their rulership over the earth comprises the changes which they cause in it and the power of bringing about the existence and deterioration of all things in the lower world since the sun, by its rule during the day, causes the sprouting, the propagation and the growth of all the warm and dry things, while the moon by its rule increases the springs and the oceans, and all liquid and cold things. Therefore He said in a general way, And to rule over the day and over the night, because theirs is the dominion over things in the lower world.
It is possible that the rulership given to them contains also a power of emanation for they are the leaders of things in the lower world, and with their power, every ruling power in nature holds sway. Thus the constellation which comes up by day rules during it, even as it is written, The sun and the moon and the stars… which the Eternal thy G-d hath allotted unto all the peoples. And this is what Scripture means when it says, He counteth the number of the stars; He giveth them all their names, likewise, He calleth them all by name. For the calling of names signifies the differentiation in their respective powers, giving to this one the power of justice and righteousness, and to that one the power of blood and the sword, and similarly all other powers, as is known in astrology. And all is done by the power of the Most High and in accordance with His Will. Therefore it says, Great is our Lord, and mighty in power, for He is greatest of all and mightiest in power over them. And similarly it says, He calleth them all by name by the greatness of His might and the strength of His power. In accord with the secret I have hinted to you, the matter of rulership is completely true.

ולהבדיל בין האור ובין החושך, between the period when light begins and the period when darkness begins. Sunrise is the period when light begins, whereas the clear visibility of the stars in the evening is the period when the darkness begins.

ולמשול ביום ובלילה, in order to bring new creatures into life in the “lower” regions of the universe, i.e. these living creatures, as opposed to the plants, required more than the light G’d had created on the first day. Seeing they are more important and more sophisticated beings they require exposure to better light in order to flourish.

ולהבדיל בין האור ובין החושך, to establish clear demarcations amongst the inhabitants of the lower regions of the universe, between when these respective luminaries were to shine, and when they were to set, i.e. to disappear from view. Basically, the meaning is the same as in verse 14 above.

ולמשול ביום ובלילה, the one, i.e. the sun by day, and the other, i.e. the moon, to govern by night.

ולהבדיל, from the time the sun rises it is light, day, and the domain of the sun, whereas from the time the stars become visible in the sky, it is nighttime, the moon’s domain. The night is called “darkness,” even though there is some light in the sky illuminating parts of the earth in a fashion.