Charles Hodge (d. 1878) spoke about Christ’s twofold kingship like other Reformed theologians spoke of it (see here). Hodge said, “Christ exercises his royal authority, so to speak, in different spheres.” Here’s a summary of Hodge’s discussion, found in his Systematic Theology, III.XI.3-4.
1) Christ’s dominion over the universe. Christ has what theologians are accustomed to call his kingdom of power. As theanthropos (God-man) and Mediator, all power in heaven and upon earth has been committed to his hands (Matt. 28:18; cf. Eph. 1:20-22, 1 Cor. 15:27, Heb. 1:13, 2:8, Phil. 2:9-10). The person to whom ‘all things’ are to bow the knee is Jesus, not the Logos, but the God-man. It is in virtue of this dominion over the universe that Christ is called Lord of lords and King of kings, i.e. the Sovereign over all other sovereigns in heaven and on earth. This universal authority is exercised in a providential control, and for the benefit of his Church. Under the present dispensation (era)… Christ is the God of providence. It is in and thorough and by him that the universe is governed. This dominion or kingdom is to last until its object is accomplished, i.e. until all his enemies, all forms of evil, and even death itself is subdued. Then this kingdom, this mediatorial government of the universe, is to be given up (1 Cor. 15:24).
2) Christ’s spiritual kingdom. Besides this kingdom of power, Christ has a kingdom of grace. He is the king of every believing soul. He translates it from the kingdom of darkness and brings it into subjection with himself. Every believer recognizes Christ as his absolute Sovereign; Lord of his inward, as well as of his outward, life. This kingdom of Christ over all his people is exercised not only by his power in their protection and direction, but especially by his Word and Spirit, through which and by whom he reigns in and rules over them. The kingdom of grace in this era is temporary; when Christ returns it will become a kingdom of glory (consummated, the kingdom of heaven).
Of course, Hodge says more on this topic; above is a summary. If you want to read more on how Reformed theologians made the kingdom of power/kingdom of grace and glory distinction, see The Reformed Scholastics on the Regnum Christi, Kuyper and Kingdoms, Bavinck on the Two Kingdoms, and “How to Obtain the Kingdom of God.”