A mutagen is something that causes changes in the DNA, while a carcinogen is something that causes cancer. A mutagen can be a chemical or a phenomenon such as ultraviolet radiation. Overexposure to UV radiation has been linked to skin cancer.
Other known mutagens include formaldehyde and dioxane. Unlike cancers, mutations are not necessarily harmful. Some mutations affect parts of the organism's DNA that serve no function. Some mutations, such as resistance to insecticides, are helpful.
Mutagens and carcinogens are related to each other in that most carcinogens are also mutagens. One theory is that cancer is caused because cells in the body undergo mutation.