Radiation Oncology deals w/ using radiation as a tool to treat cancer (ex: somebody has stage III cancer of cervix and a radiation oncologist zaps her w/ strong radiation to kill the cancer, like around 10-20 treatments 3x/week for 1 month or so). This is one of the big 3 ways to treat cancer, 1) surgery 2) chemotherapy 3) radiation
Usu an oncologist will refer a cancer patient to a Rads Onc to get the treatment.
Nuclear medicine is a branch of Diagnostic radiology, and deals w/ using radioisotopes (remember chem class) w/ imaging to visualize anatomy/physiology/pathology of the body (ex: getting a PET scan to look for metastasis of cancer to brain, liver, etc; or using radiolabeled Iodine to assess the uptake of I- from the thyroid gland in a suspected Hyperthyroidism patient).
Usu some physician will refer a patient to a nuclear medicine doc to get a specific test done.
This is not a 100% complete answer, but is a general overview of the two specialties.