What's the difference between being cancer-free and in remission?

They're the same. Different doctors use different terms to mean different things, but if you are cancer-free you are in remission. If there is little to no chance your cancer will come back, you might be considered "cured". Ask your oncologist what he or she means when using these terms!
Remission as a term . Is properly used in leukemia, while being cancer free applies to solid tumors that were removed, and there is no evidence of residual.