Hematology and medical oncology are two separate specialties, but for traditional reasons, in the US physicians choosing these fields most of the time train in both. (In Europe and Asia they are completely separate) So as a hematologist I see all kinds of diseases of the blood, including leukemia, lymphoma, etc, as well as anemia, clotting disorders, and bleeding problems (such as hemophilia). As an oncologist, I basically treat all sorts of cancer, including liver and kidney tumors, and of course the more common ones such as breast, colon, and lung cancer.
Glad to hear your mother in law is OK! It's a pretty small world, I did my heme/onc training in MD Anderson (lived in Houston for 6 years).
And don't worry, general medical questions are on the house! :-D