The Edit Defaults option is very similar to the Edit Preview, however here you are editing the actual default values for your properties.
When you make changes to the values in this mode, you may notice the preview out of date warning in the viewport (which will go away once you click the Compile button).
The Public View option is a toggle that can be used to filter the variables to only show ones that have been marked as Public or all variables.
Above, the variables IsInAir? and Reloading have been defined as Public so only those are the only ones that appear in the Anim Preview Editor when Public View is enabled.