If all the cancer cells and precancerous cells (cells with some of the mutations needed to be cancerous but not all) are dead, you can get a new cancer from new mutations, but it's not more likely than before you got cancer. It's not the cancer coming back, it's a new one. Killing the precancerous cells is easier than the cancerous cells because they are localized around the main tumor. They can't go through metastasis and move away. They are killed when the main tumor is removed or destroyed with radiation.

Often not all cancer cell are dead, that's why the cancer comes back. Then it's the same cancer. Even if it appears in a different location, it's still the same one, it just got to the new place through metastasis.