Yup - they are two mutually exclusive tracks. Doing a hemepath fellowship doesn't allow you to see patients in house and give chemo. You can generally do bone marrow biopsies, and there is the rare hemepath doc who sees patients occasionally - generally someone who has a specific rare interest and does it as part of research and their expertise. But your time is spent reviewing bone marrow, lymph node, and peripheral smear slides (to diagnose cancer or other diseases) and interpreting other lab results like flow cytometry. You do a hemepath fellowship out of path residency - as far as I know you can't get a hemepath fellowship coming from a different field.
Heme-onc you do after medicine residency, and again I don't think you can do this unless you have done medicine residency. Surgeons have surgical oncology, another fellowship, if they choose.
Amazing that your school hasn't informed you about this...I know some schools marginalize path and act as though diagnoses are easy to make, just snip the tissue out and put it in a magic box and voila, but sheesh.