In the "sermon on the mount", Jesus refers to the kingdom of heaven and what it takes to get there. He says that it’s harder for a rich man to enter the kingdom of heaven than for a camel to pass through the eye of a needle. The eye of a needle was actually a nickname for one of the entrances into Jerusalem’s temple walls, but nevertheless he says through God all is possible. That right there should tell people willing to look that there might be a difference between the kingdom of heaven and everlasting life. If one goes to Jesus, rich or not, they will have everlasting life. Nowhere does it say you have to believe upon Jesus to get into the kingdom of heaven. Jesus explains what it takes to get there in the sermon on the mount. Men with their incompetence refused to look into that there was possibly a difference between everlasting life and the kingdom of heaven, even though Jesus did say that heaven and Earth shall pass away. In place there will be a new heaven and a new Earth. Jesus also said in his father's house there are many mansions. That word "mansions" in the original Greek is the word "μονη" (moh-nee), which really means a residence or resting place. Heaven as it stands now is just a temporary holding place for those who've lived their lives honorably, including those who believed in our Messiah. Knowing there is a difference between everlasting life and the kingdom of heaven will answer that question that atheists and doubters love to bring up, “if no one has ever heard of Jesus, why can’t they get into heaven?”
In order to achieve everlasting life, one must go through Jesus. God will not judge against those who are not held accountable for what they don’t know. If they live their lives the way Jesus described in the sermon on the mount, even if they never heard of him, they will get to the kingdom of heaven after their death. There will be a time for them to make that choice in the future, which I will get to later. Those who have lived their lives wickedly will not get into the kingdom of heaven, but at some point in the future can find themselves making the right choice and achieving everlasting life after they have learned their lesson. They are the ones who are called "the dead" in Revelation 20 who live not again until the thousand years are done. Every single time when the term "everlasting life" is mentioned, it talks about believing upon our Lord. So why the difference in what it takes to get to the kingdom of heaven and what it takes to achieve everlasting life? Because it's two different things.
There is another age after this one, as I’ve written many times before. When Jesus returns, as is written in the original Greek, he will end this age. Not the world. In Matthew when it speaks of the end of the world, in each instance that word in the original Greek wasn’t “cosmos”. It was “αιων” (ahee-OWN), which is their word for age. There are times in Matthew when the word “world” is cosmos in the original Greek, but when it speaks of the end of the world, it’s always “αιων”, so there's a reason why he used different words despite the translation of the KJV. Without the knowledge that Jesus' return only ends this age, Revelation 20 cannot be made sense of. Keeping in mind that when Jesus returns he ends this age, go read Revelation 20 again and you will get a very new sense of it. The correct sense I am hoping 
It will be then when those who haven’t made a choice or those who’ve made the wrong choice will have to make it. The ones who made the wrong choice or lived their lives wickedly will not live again until the thousand years are fulfilled. They are called “the dead”. Satan will be loosened from his bottomless pit prison and will try to deceive the world once again. Those he deceives then will lose their last chance at showing their faith to God. Everyone will know the right choice, but as is written even at the end of this age the mystery of God will be finished at the blowing of the seventh trump and still many will fall. It will be the same case at the end of the next and last age.
Now when someone mocks you for your beliefs or genuinely asks you that question about those who never had a chance to choose Jesus as the Christ how they will get to heaven, now you have your answer. Traditional teaching has failed at this probably as much as they’ve failed at anything else about God’s word. It’s amazing how many of them have refused to ask such a simple question, “is there a difference between the kingdom of heaven and everlasting life?” Without ideological blinders, you can now see there truly is a difference between the two.