There are lots of different types of radiation and not all of them increase the risk of cancer. Some cancer treatments such as chemotherapy and radiation therapy used to treat cancer through shrinking the tumors, but may increase a person’s risk of developing a different type of cancer later in life.
As Hannah points out, there are lots of types of radiation. The issue is the dose – at high levels, radiation can cause cancer. For example, in areas where people have been exposed to large doses, we see much higher rates of cancers than in other areas. So places where nuclear power plants have been damaged, nuclear bombs tested etc will be much more dangerous. That’s why most of those areas are not allowed visitors any longer, some for many hundreds of years!