To enter into the kingdom of the heavens, we need to do two things: call on the Lord and do the will of the heavenly Father. To call on the Lord suffices for us to be saved (Rom. 10:13), but to enter into the kingdom of the heavens, we also need to do the will of the heavenly Father. Hence, not everyone who says, "Lord, Lord," will enter into the kingdom of the heavens; but those who call on the Lord and do the will of the heavenly Father will enter in.
Since entering into the kingdom of the heavens requires doing the will of the heavenly Father, it is clearly different from entering into the kingdom of God through regeneration (John 3:3, 5). The latter entrance is gained through being born of the divine life; the former, through the living of that life.