Is biliary duct cancer a form of primary liver cancer?

Not usually: Bile duct cancer is cholangiocarcinoma & more often affects the bile duct outside the liver. Primary liver cancer is hepatocellular cancer and affects the liver cells.

No: Primary liver cancer is when the liver cells themselves, the hepatocytes, transform into cancer cells. Bile duct cancer is when the cells lining the bile duct transform into cancer. Primary liver cancer tends to grow large nodules in one place, and doesn't give a lot of symptoms until the tumors are large. Bile duct cancer tends to obstruct the bile ducts and create symptoms, such as jaundice.