My course IS biochem. Basically, all the biochem from a full undergraduate course, plus a ton extra, crammed into a month and a half.
But yeah, the mutations that make it replicate like nobody's business actually form a tumor out of the cells. Benign tumors are tumors just filled with these kinds of cells. Malignant tumors are tumors where the cells have mutated to escape the tumor itself, which causes cancer, because the freely replicating cells are on the loose, making tumors everywhere.
I actually was not aware that tumor = cancer until I studied this stuff.