Christian Science is not based on religious principles. it is more like a new age philosophy based on Mary Baker Eddy's "Science and Health with Key to the Scriptures". Followers of the movement believe that you live multiple lives. With each life, you are suppose to live better spiritually so can reach heaven. Traditional Christians do not usually believe in reincarnation.
The followers of Christian Science are different from "traditional" Christians indeed. Mainstream Christians do not prohibit the use of vaccinations, surgery, or medicine in any way. Although Christian Scientists believe in ethics and the Ten Commandments as other Christians do, their main difference from traditionalism is the medical aspect. This is a big enough reason that they sometimes have difficulty recruiting new members.
The followers of Christian Science do not accept the concepts of Original Sin, the Holy Trinity, miracles, the resurrection or atonement of sins. These concepts form the core of traditional Christianity, so by not accepting these concepts the beliefs of Christian Scientists are drastically different from those of mainline Christian religions.
Those who follow Christian Science are different from other Christians in that they see that the spiritual presence of Christ is able to alleviate suffering and even to heal. In today's society, they go too far when they refuse to take advantage of modern medicine, but their premise of spiritual healing is a positive one.
Yes, I believe that the followers of Christian Science are different from traditional Christians, because they have some fundamental differences in their believes. Christian Scientists reject Western Medicine. Instead, they rely on God's ability to heal. That is a major difference from Christians, who tend to accept modern medicine and vaccinations as valid healing methods.