The Kingdom of God has two aspects, the Kingdom that exists now and the Kingdom that will come at the second coming of Christ. It is also my understanding that the “Kingdom of God” and the “Kingdom of Heaven” are one and the same thing.
The NT Scriptures speak plainly about a present Kingdom as well as a future Kingdom.
Some theologians have distinguished between the two aspects of the kingdom as being grace and power. The present kingdom they say is a kingdom of grace, the final kingdom is one of power.
I don’t like distinguishing the kingdoms in that manner. It implies that the present kingdom is powerless and that the final kingdom is void of grace.
The difference rather should be that of purely spiritual nature – something that happens in the heart of each beleiver and in the Church at large – and the final kingdom being a complete and visible reign of our great king and saviour Jesus Christ.
Spiritual nature of the present kingdom:
I tell you this, brothers: flesh and blood cannot inherit the kingdom of God, nor does the perishable inherit the imperishable. (1Co 15:50, ESV)
Jesus answered, “My kingdom is not of this world. If my kingdom were of this world, my servants would have been fighting, that I might not be delivered over to the Jews. But my kingdom is not from the world.” (Joh 18:36, ESV)
The kingdom does have power:
For the kingdom of God does not consist in talk but in power. (1Co 4:20, ESV)
because our gospel came to you not only in word, but also in power and in the Holy Spirit and with full conviction. You know what kind of men we proved to be among you for your sake. (1Th 1:5, ESV)