Q. What does it mean to enter/inherit the kingdom of God? How does it differ from being saved and going to heaven?
A. Entering / inheriting the Kingdom of God and being saved and going to Heaven are equivalent concepts. In John 1:12-13 we’re told that receiving Jesus and believing in His name gives us the right to become children of God. Romans 8:17 says if we’re children then we’re also heirs – heirs of God and co-heirs with Christ. And what do we inherit? Eternal life in His Kingdom.
In John 3:3 Jesus said unless we’re born again we can’t enter the the Kingdom of God. So entering and inheriting are the result of being born again, which is the same as being saved. By being born again we become children of God. As His children we are also His heirs. As His heirs we inherit the Kingdom. Get it?