Essentially, the only thing that unites cancers together is that they represent a class of diseases in which your own cells multiply in an uncontrolled manner. Beyond this idea of "out of control growth", there are a number of common ways which these distinct phenotypes occurs (such as too much of pro-growth molecules, not enough "slow down" molecules etc) but genetically/molecularly there are many, many different routes which these phenotypes can be achieved.
This, again, is still only touching on the surface. After you have the molecular underpinnings of the "out of controlness", you have genetic and non-genetic factors relating to things like where the tumour is, how do the cells change once the cancer begins to progress, how your body reacts to the cancer, how your body reacts to drugs etc.
In 100 years time, I'm confident we'll look back on our present day way of thinking about cancer in the same way people now look back at our previous ideas relating to mental illness 200 years ago, or general diseases 500 years ago.