Should I go to cancer center and also a hematology and oncology center?

What is the problem. You did not explain why you want to go to cancer centre ?. First you should see your own local physician, who will refer to an oncologist, if it is a rare cancer your oncologist will refer you for experimental treatments in a cancer centre, or you seek a second opinion.
Hemonc in cancer ctr. When you go to cancer center- unless mentioned otherwise (i.E radiation center or surgical center) , generally speaking, you will be seen by a hematologist/oncologist or a medical oncologist. In some bigger cancer centers - in addition to medical oncologist, there would be also surgical oncologist and radiation oncologist in the same place.
Hem. Most oncologists are also board-certified hematologist. But some cancer centers do not deal with benign hematology.

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What is the definition or description of: hematology and oncology?

A speciality/of Canc. A cancer specialit is called an oncologist. Hematologists specialize in the diagnosis and treatment of blood disorders including anemias and cancers of the blood(leukeias and lymphomas). Read more...