What is medical oncologist vs heme-oncologist?

Not much. Medical oncologists are trained through to diagnose and treat cancer using internal medicine (i.e. With medications, or chemotherapy). Many medical oncologists also receive training in hematology (the study of blood diseases) since the two are closely linked - thus, they are hematology/oncology certified (heme/onc).
Very similar. Hematology refers to blood disorders, both benign and malignant. Oncology refers to malignant diseases, some of which are blood related malignant diseases. Most training programs in the us are joint hematology and oncology programs. Most community based physicians consider themselves hematologist-oncologists. In many academic centers physicians specialize in one area or the other.