The term "cult" is typically used by the secular media to describe religious or semi-religious groups whose members are controlled in almost every single respect by a single individual. Some good examples are Hare Krishnas or Scientologists.
To orthodox Christians, however, the word "cult" takes on a wider meaning. Not only can groups be considered cultic in the sociological sense, groups may be deemed cultic in a theological sense as well. What I mean is that groups which claim to be in harmony with Christianity but deny foundational Christian doctrines--such as the Trinity, or the unique deity of Jesus Christ--are cults in a theological sense. Thus, the Jehovah's Witnesses, Mormons, and Christian Scientists qualify as cultists.
Now, while the word "cult" is always used with reference to a particular group, the word "occult" is typically associated with esoteric and mystical practices. It deals with hidden or secretive means to attain personal power, and is characterized by a reliance on the supernatural to achieve its ends. The occult includes such practices as fortunetelling, witchcraft, or trance-channeling--the sort of thing described in Deuteronomy 18. Additionally, tarot cards, crystal balls, ouija boards, and horoscopes number among the many tools which are used by occultists. Clearly, the occult deals directly with demonic forces.
It should be clearly noted here that there is some cross-over between cults and the occult in that some cults, such as the Church of Satan and others, are also clearly involved with occult practices. However, not all cults indulge in the occult. For example, it would be unfair to link the Jehovah's Witnesses and the United Pentecostal Church in an overt sense with the occult. Now, while a clear distinction should be drawn between the terms "cult" and "occult," we must keep in mind that they are both connected with teachings which oppose the Word of God.