KDb is consisted of a general-purpose C++/Qt-only library and a set of plugins. Because there is no dependency on Kexi, Calligra or even on KDE libraries, KDb is developed for a wider audience. Kexi since the version 3 uses it too, thus deprecating KexiDB.
Unlike QtSQL, KDb 'knows' how to create database and new tables. It has a Qt/C++ API for that. There is no need to pass SQL at all but you can pass if you wish (it will silently parse your statements before contacting the database). KDb is developed as a next generation database handling layer for Kexi and similar complex apps.