Data connections enable you to select and load data from a data source. All data connections are managed centrally from the QMC. Data connections are created in the Qlik Sense data load editor. The user who creates a data connection automatically becomes the owner of that connection and is by default the only user who can access the data connection. The data connection can be shared with others through security rules defined in the QMC.
When you import an app developed on Qlik Sense Desktop, existing data connections are imported to the QMC. When you export an app from a server, existing data connections are not exported with the app.
With analytic connections you are able to integrate external analysis with your business discovery. An analytic connection extends the expressions you can use in load scripts and charts by calling an external calculation engine (when you do this, the calculation engine acts as a server-side extension (SSE)). For example, you could create an analytic connection to R, and use statistical expressions when you load the data.
Extensions can be several different things: A widget library, a custom theme, or a visualization extension, used to visualize data, for example, in an interactive map where you can select different regions.