Is the church and the kingdom the same thing?
Often the Bible explains things through multiple words whenever one word is insufficient to fully describe what is meant. After all, the Bible is trying to describe a world that we cannot touch or see. For example, Jesus is described as the good shepherd, the door, the way, the truth, the light, the king, the son of man, the son of God, and many other words. Who he is and what his job entails are too complex for any one description to be good enough to get across the whole concept.
The kingdom and the church are in some ways talking about the same thing, but one term alone doesn't explain it well enough. In English, we tend to use the terms as if they are talking about the same thing, but in reality, there is a difference.
The meaning in Greek behind the word that is translated "church" is "the called out" ones. It can be thought of as a word focused on the people who were called out of one state and into another. In the spiritual sense we are called out of darkness and into the light (Ephesians 5:8). Church, therefore, implies the relationships that we have with one another and with Jesus because we are united in a sense of commitment to righteousness.
The kingdom is more about authority. Kingdoms exist to establish law which allow people to live peacefully together. When we enter a kingdom, we agree to be obedient to the laws of that land. If we misbehave, we can expect to be punished or thrown out of the kingdom. In this sense the kingdom is about the place, the authority and the boundaries. However, in the Bible it is a spiritual place and not a physical one (Romans 14:17). Thus, in John 3:3-5 when Jesus was talking to Nicodemus about the kingdom, he mentioned that it could not be seen nor entered without a change in the person. We can see the people who make up a church, but outsiders cannot see the kingdom. That says they are not the same thing, even though those in the church are those who have entered the kingdom.
Notice some ways in which the two terms are used or not used. In Acts 8:12, it says, "… as he proclaimed the good news of the kingdom of God …". It did not say that he was proclaiming the good news of the church. In fact, it would be hard to make sense of it if it did say that he was proclaiming the good news of the church. The church is the people and the good news is not about the people who are in it. The good news is about the kingdom, which is a marvelous place to go to that has perfect laws and a perfect ruler. We know it is a wonderful place because passages, like I Corinthians 6:9 and Ephesians 5:5, say that evildoers cannot get in.
Also in a passage like Acts 8:3 where "Saul began to destroy the church" would not make sense if we tried to substitute the word "kingdom." The church is the people and it is possible to kill people because the church is in the visible realm. But Saul could not destroy the kingdom because it is a place that is not in the visible realm.
Of course, because of our sin we all are on the outside and are not allowed in. That means that we have to change our ways and get forgiveness in order to enter the kingdom. If we manage to enter the kingdom (the place with laws and a king), then that means that we are then in the church (the company of people who have also entered). That is why it is important to notice what the Scriptures teach is the way to see the kingdom (John 3:3) and enter the kingdom (John 3:4). Some people think that because they go to the right building that they are in the right church. Buildings in the physical realm have nothing to do with it because all the important stuff is in the invisible realm. It is also very possible to join ourselves to a church and never have entered the kingdom in the first place. That is because the church that we see is not an accounting of those who actually found and entered the spiritual kingdom. It includes the righteous, but it also includes the hypocrites. If we focus on entering the kingdom, then we will be in the right church.