A cult is a religious organization that says it's Christian but denies one or more of the fundamental truths of Christianity. These would include monotheism, the Trinity, the inspired reliability of the Bible, Christ's deity and humanity, or salvation by faith. They are usually dominated by one overbearing, dictator-type leader, use abusive forms of authority, and exploit the members financially and often sexually.
A sect is a Christian group that is basically sound in its preaching and teaching, but has elevated some secondary doctrine, peculiar tradition, or unique practice up to such a level of importance that the group breaks fellowship with other believers. Examples of this could include foot-washing, modes of baptism, or opinions about the time of the Rapture.
Cults are not Christian at all, even though they claim to be. For example, the Church of the Latter-Day Saints (Mormon) is not a Christian organization. Sects are Christian but they're divisive over secondary issues.
For example, the Missouri Synod Lutheran Church forbids its members to take Communion with any church but another Missouri Synod Lutheran church. If a Missouri Synod Lutheran was to break bread with us at our church, he or she would be excommunicated by the Missouri Synod. The Lutheran policy seems to say that no other Christian churches are "real" Christian churches, but that we're all heretics. This is the sin of sectarianism. Paul talks about this in 1st Corinthians 1.
Both of these are bad, though cults are worse because they actually deny the faith, where sects unbalance the faith. However, a spirit of denominational superiority, church-splitting, and judging one another over matters of personal conviction, weakens the Body of Christ and makes us more vulnerable to Satan's attacks.