Perhaps the most important difference between bacteria and viruses is that most bacteria do good work while viruses are parasites that will kill you if you let them. In both cases dead or weakened types can be used to create vaccines to help prevent illnesses caused by the specific kind one may be exposed to.
Bacterial infections are usually localized while a viral infection spreads throughout the system. There are enzymes found in both, but bacteria are much larger than viruses and easier to spot.
According to information put out by the Mayo Clinic, Bacteria are living organisms, but viruses are considered living or non-living. One characteristic of living bacteria is that it contains DNA and RNA as in every other living organism. A virus can be single-stranded and circular or linear and contained in a protein coat or envelope that makes them relatively impervious to antibiotics, but bacteria are always looking for interaction with the environment and are usually covered by a cell wall or capsule of slime, to that end. Bacteria are double-stranded and circular in shape.
What they do have In common is that they can both cause disease in humans and animals although it is difficult to know whether a virus or bacteria are causing any particular flu or infection until antibiotics have been tried and have failed, in the case of a virus. Symptoms are localized with a bacterial infection but generalized to an entire system with a virus. Sometimes symptoms can appear similar, but viruses cannot be killed with antibiotics since they produce their own antibodies to combat them. One can only treat the symptoms and get enough rest so the body can fight off the virus itself.
Since bacteria are large simple targets it is relatively easy to cure infections with antibiotics. This Animation may clarify the actions of a virus.
Note that the virus attacks bacteria as it would any living host. In specific conditions viruses have been known to target cancerous brain tumors and clear them of malignant cells, so the news isn't all bad about viruses either, but such instances are anecdotal and not part of the general approach to serious diseases like cancer.
Whatever the condition, it is important to treat it correctly since bacteria can build up resistance to antibiotics, just as we build up a resistance to disease that may attack us.