The larger field of vision make the more visual difference between the different projection.
The example show a field of 150° and 360° wide using the different options available in the menu Setup -> Chart, Coordinates
When you click the “Show all sky” button the projection automatically change to the ARC full sky show below.
This same change of projection occur if you use simultaneously: an oblique projection, an azimuthal coordinate system, a very wide field of vision, and the altitude at the chart center is greater than 45°.
It return to your selected projection if you zoom in or move the chart center nearer the horizon.
On smaller field of vision the difference between the projections is more subtle but important if you want to match a specific image.
The example here show a FOV of 70° to make some difference visible at this scale, look at the grid curvature for more evidence.