The two systems are actually related. The I through IV groupings are actually defined using the TNM system. Cancer that recurs after all visible tumor has been eradicated, is called recurrent disease. Disease that recurs in the area of the primary tumor is locally recurrent, and disease that recurs as metastases is referred to as a distant recurrence. Distant recurrence is often treated similarly to stage IV disease.
Some types of cancers use different staging systems.
For many other cancers the staging is further divided with classifications like IIa, and IIIb. For leukemias and other cancers which don't form solid tumors the staging is again different. The best source for this is your doctor. It is important to know that while stages are an important guide to treatment and prognosis, they are certainly not the whole story. For instance, if a patient with kidney cancer has only one metastasis, it can be removed surgically, and the prognosis is much better than if he had many metastases.