Tumor, neoplasm, malignancy, cancer can all denote an abnormal growth or mass of tissue.
Tumor , the most general term, is applicable to any such growth or mass in or on the surface of the body of a human being, animal, or plant.
Neoplasm often replaces tumor in technical use when the reference is specifically to a more or less unrestrained new growth of cells that serves no physiological purpose or to a mass formed by such growth.
Malignancy in application to a neoplasm denotes a growth that because of unrestrained proliferation and tendency to spread and invade other tissues constitutes a danger to life. This use, though deplored by some purists, is common in technical literature and often used euphemistically in discussion with a patient or his associates.
Cancer is the usual popular and technical term for a malignant neoplasm, though sometimes it is applied specifically to such neoplasms arising in epithelial tissues (as skin or membrane) which are more often distinguished as carcinomas from the other great class of cancers, the sarcomas , that originate in nonepithelial tissues (as bone, muscle, or connective tissue).