Is there a difference between cancer and tumor?

Yes. While cancers are characterized by tumors, not all tumors are cancerous. Tumor derives from the latin for a 'mass' (a 'lump' - not all of which can be felt of course). Tumors are a result of an abnormal growth of cells and can be benign, or essentially only grow in one place and cannot spread. Cancer is when a tumor becomes malignant, or is able to spread and invade other tissues.
Yes and No. Sometimes a tumor is benign (not cancer), but most people mean cancer when they say tumor. It is possible to have benign breast and uterine tumors. Another word that is often used is mass. Mass usually means we are not sure yet if it is malignant.