For centuries the church has taught that to be a Christian one had only to believe that Jesus is the Christ, that he was risen from the dead, and that he is their Lord and Savior. This notion came from interpreting scriptures such as John 3.16 that reads: "For God so loved the world that he gave his only Son, so that everyone who believes in him may not perish but may have eternal life." This "believing in him" meant that the believer was guaranteed a spot at the heavenly banquet table, i.e., they were "saved." And it has long been assumed that if one was "saved" then they were a Christian.
This notion was so prevalent that during the Reformation in the 1500s, Martin Luther tried to have the letter of James removed from the Bible because James puts a high emphasis on doing good deeds to show the believer's faith: "What good is it if you say you have faith but do not have works? Can faith save you?" (James 2.14). The reality is the New Testament does indicate that faith can "save" you and Luther wanted James expunged from the Bible because of the assertions that more might be required.
But does faith or belief makes someone a Christian? The answer is resoundly "no."
Scripture does make it clear that belief is enough to get someone into heaven. That chorus is played again and again and again (Mark 16.16; Luke 8.12; John 1.12; John 3.15-18; Romans 10.9-10, et al). On the other hand, nowhere in scripture does it say that a believer is a Christian. A Christian is, by definition, someone who is a follower of the teachings of Christ. In the vernacular of scripture, a Christian is a disciple of Christ.
Just because you believe in something doesn't mean you're a devotee. For instance, you can believe in football all year long. You can go to games, buy the uniform, and even sit on the sidelines. But unless you play the game, you're not a player. The same is true of a Christian. Someone can believe that Jesus is the Christ. That makes them a believer. But a believer is not necessarily a player, a follower of the teachings of Christ. In other words, a believer isn't necessarily a Christian.
So, what is a Christian? Well, first of all a Christian is a believer, but a Christian does more than simply believe; they commit themselves to be a follower of Jesus and his teachings. John 1.12 says that those who believe have the "ability" to become the children of God. 1st John 2.4 tells us, "Whoever says, 'I have come to know [Jesus],' but does not obey his commandments, is a liar." It's clear that obedience is the mark of one who is a true follower of Jesus.
So, what does it take to be a Christian? Jesus gave two great commandments and one great commission. The two commandments are to (1) love God; and (2) to love one another (Matthew 22.37-40). The great commission is to proclaim the gospel and make disciples (Matthew 28.19-20). These are the bottom line marks of a Christian: do they demonstrate love to God and to all people? And do they "bear fruit" -- are others becoming Christian through their words and deeds, and then are they teaching them to be disciples?
If someone isn't consistently showing love to all (particularly to the poor, the oppressed, the prisoner, and the sick -- Matthew 25.34-36), then they may be a believer, but they're not a Christian. And if someone isn't bearing fruit, if they're not helping people discover the Kingdom of God, then though they may be a believer. . . .
Clearly, not everyone claiming to be a Christian really is. Jesus knew this when he said, "Not everyone who says to me, 'Lord, Lord,' will enter the kingdom of heaven, but only those who do the will of my Father in heaven" (Matthew 7.21).
The definition of a Christian is: they're a disciple of Christ, a follower of his teachings, and obedient to Christ's commands. There will probably be many believers in heaven, but Christians are special -- and unfortunately, they're quite rare.