cancer vs leukaemia

cancer and leukaemia both are nouns.

Word	Noun	Adjective	Verb	Adverb
cancer	Yes	No	No	No
leukaemia	Yes	No	No	No

As nouns, leukaemia is a hyponym of cancer; that is, leukaemia is a word with a more specific, narrower meaning than cancer:

cancer: any malignant growth or tumor caused by abnormal and uncontrolled cell division; it may spread to other parts of the body through the lymphatic system or the blood stream
leukaemia: malignant neoplasm of blood-forming tissues; characterized by abnormal proliferation of leukocytes; one of the four major types of cancer

Other hyponyms of cancer include lymphoma, carcinoma, cancer of the blood, leucaemia, leukemia, sarcoma.

cancer (noun)	leukaemia (noun)
any malignant growth or tumor caused by abnormal and uncontrolled cell division; it may spread to other parts of the body through the lymphatic system or the blood stream	malignant neoplasm of blood-forming tissues; characterized by abnormal proliferation of leukocytes; one of the four major types of cancer