Cancer cells themselves are not effective transmissible agents of disease in humans. Unlike infectious pathogens, there is not a suitable receptor for adhesion at an exposed or accessible site, a suitable environment for replication, and adaptions for immune escape by the tumor cells. There are exceptions in other species: tasmanian devil, dogs, and clams. Importantly, in all of these cases, transmission to another species has not been demonstrated. Eventual transmission to another clam species may be more likely to occur, though, because, unlike vertebrates, they are not known to have a self/non-self recognition system.
Humans, though, do have a self/non-self recognition system. Even if we ignore the requirement for receptor binding and invasion, consider what happens when cells from another species, and even another human, are surgically implanted. Without immunosuppression, these non-self cells are rapidly attacked and destroyed.
With immune suppression and surgical implantation, though, you can see transmission of cancer. Donor-related tumors in transplant patients are still rare, though the low frequency of transmission may be due, in part, to screening. The fact that we see this at all demonstrates the significance of transmission route and immune escape.
Cancer cells do, of course, metastasize within a single human individual. In order for a tumor seed to successfully metastasize it does need to evade the immune system, find an environment suitable for replication and adhesion. This, however, requires tumor associated cells, non cancerous cells that regulate the microenvironment to make it favorable for growth and replication. You can read about them in Hanahan and Weinberg's 2011 review.
The requirement for tumor associated cells and a permissive microenvironment might be why, in a problematic series of experiments at Sloan Kettering in the 50s, when subjects were inoculated with tumor cells, the procedure resulted in growth of the new tumor, recurrence after excision, and death in some cases where the subject had pre-existng cancer. Transplantation into healthy subjects (yes, they did this) resulted in nodules that spontaneously regressed. This experiment has since been interpreted as evidence for immune system control of transplanted tumor system in healthy individuals, as compared to growth and progression in a receptive niche in a cancer patient. In this example as well, you have eliminated the need for a natural mechanism for adhesion and invasion, and these are same species cells.