Active immunity is the creation of an immune response to a foreign antigen, providing long term immunity through antibodies.  Vaccines, such as that for Hepatitis A, generate an immune response to prime the system for future exposure. 

Passive immunity, on the other hand, provides short term protection because it only lasts as long as the acquired immunoglobulin does.  Examples include the igG transferred through the placenta, IgA presented in breast milk, and antivenom delivered after snake bites. 

The Venn diagram below does a nice job drawing boundaries between the two types of immunity and highlights their similarities

http://occmed.oxfordjournals.org/content/57/8/552.long

http://creately.com/diagram/example/hf158ro6/Active%20vs%20Passive%20Immunity