What exactly do the sequence settings do?
The entries for the creation of a new sequence are only presets.  They load things like pixel pitch, resolution, color depth, etc.  Many of these can be changed after creation, particularly if you haven't added anything to the timeline yet.  You can also make additional presets if you have frequent use of settings that there isn't already a preset for (or you can even manually select all the settings and not use a preset.)

This is the actual sequence settings:



As you can see, the framerate(timebase), frame size, pixel pitch (aspect ratio), fields, display format, audio sample rate and audio display format make up the primary settings.  

There are additionally settings for how previews are rendered, which particularly matters if you intend to use previews in the rendering of final output, otherwise it just impacts what you see during editing (after preview renders have finished.)

While you can export in different formats, that will result in scaling if the resolution differs.  The sequence settings determine how the video renders, the export settings determine how the rendered frames are saved in to a final output.