You can set up how you want Quick Search to work in your company.
In Admin -> General Setting -> Header you will find a section for the setting of Quick Search.
The default setting is that Quick Search will search in whatever Filter or Favorite you have selected.
This means that it will search in whatever list of Styles or items you see.
If you change this to search in "All style or items" Quick search will search in all not closed Styles or Items across filters and favorites.