In Reformed church history, theologians have generally made a distinction when it came to discussing God’s kingdom or kingdoms. Simply put, historic Reformed theology distinguished between God’s general kingdom (his kingdom of power/nature) and God’s saving kingdom (his kingdom of grace/glory). Here’s how Herman Witsius spoke about this distinction in his discussion on the second petition of the Lord’s Prayer: Thy kingdom come.
The kingdom of God must be viewed by us in a twofold aspect, as universal and as special. I use the phrase, universal kingdom, to express his boundless greatness, majesty, authority, and power over all. “The Lord hath prepared his throne in the heavens; and his kingdom ruleth over all.” This is the kingdom to which the sun with all the stars, the sea with her waves, the winds with all their tempestuous fury, the seasons of the year with their various changes, the alternate returns of day and night, all the empires of the world, though engaged in acts of mutual hostility—are subject….
…Besides this universal kingdom, or, as it may be called, the kingdom of nature, God has constituted a special kingdom over his people, expressly elected for this purpose. This, again, is either the kingdom of grace in this world, or of glory in the world to come. The kingdom of grace may be likewise subdivided into the two economies of the Old and New Testaments. Under the Old Testament God was certainly the king of the people of Israel. …The form of political government established among the children of Israel was entitled in every way to the name of a theocracy. …In the Gospel…the kingdom of God is scarcely ever used in any other sense than as denoting that state of dignity and freedom which belongs to the church of the New Testament under the reign of the Messiah.
[In the second petition of the Lord’s Prayer, the kingdom] is neither the universal kingdom of God, nor that kingdom which he had in a peculiar manner over ancient Israel, but the kingdom of God as it was to be manifested under the economy of the New Testament.
For Witsius’ entire discussion of “Thy kingdom come” see “Dissertation 9” in his Sacred Dissertations on the Lord’s Prayer.