First, we must clearly understand what Active and Passive Immunity are, respectively.
Active Immunity involves antibodies that develop in an individual's immune system. These antibodies develop after the individual receives exposure to a specific antigen. Active immunity takes place by way of exposure to a disease. In addition, it occurs when one receives a vaccination.
An individual acquires Passive Immunity via the transfer of antibodies from one person to another. This kind of immunity comes from mother to child through the placenta prior to birth. One can also receive it in a medical situation. This is from blood products that contain antibodies.
The general difference between Active and Passive immunity is that Active Immunity is long lasting. Passive Immunity, in contrast, is of a shorter duration (a few weeks or a few months).
First, the similarity of passive and active immunity is that they are both processes where an antibody (defense) is created by the body as a result of the reaction that occurs when a foreign antigen is present.
In active immunity, a healthy individual is given a vaccination containing an antigen that causes a disease, such as the flu virus, hepatitis, diphtheria, tetanus, or tuberculosis.
The purpose is that the individual's own body will trigger the neccesary defenses (antibodies) to fight down the antigen and remain healthy. It is basically a battle between antigen/antibody where the antibody is expected to come out stronger than the antigen.
In passive immunity there is also mediation involved but not through vaccination. In this case, the defenses are transfered automatically and sometimes merely neutralized to avoid infection.
An example of passive immunity occurs during pregnancy where the mother transfers antibodies to the fetus through the amniotic fluid. This is the natural way of for babies to acquire defenses for common illnesses when it is impossible to actively vaccinate them.