I want to know what is the difference between liver cancer and cirrhosis of the liver?

Could be the same: Liver cancer can arise from other organs (secondary metastasis) if there is another primary cancer (i.e. From the GI track, lung cancer, etc) however, in those with cirrhosis, the most common primary cancer of the liver is hepatocellular cancer (hcc). With chronic liver inflammation from liver disease, scarring occurs over time leading to about a 5% risk of hcc developing per year with cirrhosis.

Cancer vs. benign: Primary cancer of the liver, or cancerous tumors that spread from another site to the liver, are malignant growths. Cirrhosis is a benign condition of the liver from alcohol abuse or hepatitis virus, among other causes. Cirrhosis can lead to liver failure or even cause primary liver cancer.