Advice? When cancer metastasizes, are you diagnosed with cancer again or just that it spread?

Same cancer. This means the cancer has spread but it is still the same cancer.
Spread. People often refer to metastatic disease as cancer that has "come back". In fact, it really means that the cancer cells have reached a size by which they have finally "flown above the radar" and can be detected by current tests. When a cancer is surgically removed, the cancer should no longer be able to spread. Chemotherapy is designed to kill these cells that may be out there but undetectable.
It spreads. Metastasis means cancer has spread to other parts of the body, away from the site of origin. When this happens, it is the same type of cancer but that it just speads. For example, when brest cancer spreads to the liver or lungs, the cancer in the liver or lungs is still breast cancer and not liver cancer or lung cancer.