This picture shows a flowchart of Campaigns and Quick Campaigns in CRM 2013:
Figure: Campaign VS Quick Campaign flowchart.
A Campaign can extend over a long period of time, with potentially multiple different media types being used for a common purpose. It has extensive meta-data to both plan activities and then show reports on results. e.g.
A Quick Campaign, however, is for a one-off distribution of emails to a targeted group of contacts. e.g.