A One Time Snapshot campaign will role, as its name states, just one time. Choosing this option will only allow you to analyze a snapshot of the links and social-shares for your website and those of your competitors.
The setup of a One Time Snapshot campaign will require you to go through 4 easy steps, that include: adding your website, adding competitor websites, link analysis and campaign settings. All these steps are described in Setting a Campaign -> One Time Snapshot.
A Recurring Campaign will do the same thing, only that it will repeat the whole process on a weekly basis, and besides that, it will allow you to monitor Google, Yahoo and Bing page ranks. See details in Setting a Campaign -> Recurring Campaign.
You will have access to the extra modules Rank Tracking and Link Management, where you can monitor your ranks and most important links.
Each of these two phases is best suited for certain actions.
A one time snapshot is recommended for singular analyses. These may include client pitches, site benchmarking or various competitor analyses.
Recurring campaigns are recommended for the continuous analysis of your website, of your clients websites, and of your most important competitors (and client competitors). Also, this type of campaign can be used for more in-depth pitches that also require a campaign history.