That's right.
Christianity is founded on the life, teachings, death, and resurrection of Jesus Christ and he didn't advocate violence, didn't use violence and didn't lead armies into battle, which would mean that killing must be wrong from a Christians point of view.
Islam is founded on the life and teachings of Mohammad and he used violence and conquest to spread the word of Islam, he lead armies into battle that resulted in the deaths of thousands of people.
Can you see the difference and understand why groups like IS believe they are just following the examples set by Mohammad.