What's the difference between the keyboard shortcuts and + S?
I seem to be able to find applications, documents and settings in both of the dialogs.
opens the start menu:
+ S opens the "Search Windows" dialog:
Historically the + S key opened the Windows search box which was not part of the start menu. Now they are effectively the same thing almost so there is not much difference in Windows 10.
The only real difference is the fact that through the + S key, you won't see the apps but the search instead.