Word does not have the term "Quick Style Set"
It is not used on the domain Welcome
Ed Bott didn't use such a term in Microsoft Office Inside Out:2013 Edition, published through MicroSoftPress.
It seems to be your own creation despite no precedent from MicroSoft, Sarah Barnhill or anyone else.
However, the term is used in a Youtube video for a different item. https://www.youtube.com/watch?v=liQFbLo9Cx0, which is also applied incorrectly.

Even when Right Clicking on the style to add to the Gallery, it is "Add to Style Gallery" or through the modify style window, "Add to the Styles gallery"

Style Sets are listed in the Design Ribbon. A Style Set can be selected. Hovering over a Style Set will give the name of the Style Set. If you open the Style Pane and show All Styles, it can be more apparent that even those styles not in the Styles Gallery change. Since most of MS styles are still similar, it can be more obvious if a Style is edited so the preview change is even more obvious.
OR, you can remove ALL the Styles from the Gallery and then Change the Style Set on the Design Ribbon. Your statement indicates then that NOTHING will change because none of the Styles are in the Gallery.