Well, to clarify...
Joomla! 1.5 has a completely redeveloped framework API. This framework makes many tasks simpler for PHP developers - i.e. working with files, interacting with an ftp server, working with arrays, managing sessions, HTML forms, internationalization, database access, user tracking, dates, event handling, caching and more. This is the Joomla! framework.
For a diagram, see:
http://dev.joomla.org/content/view/1137/80/Applications are built on top of the framework. The three applications you are probably most familiar with are the site application and the administration application. The former is what site visitors most often see, and the latter is what site administrators use to manage the site.
In general, the framework API is available no matter what application you are using, though there are still some classes that need special work to use in the frontend or backend (i.e. they are specific to one or the other).
Each application has some classes and infrastructure in addition to the framework. JToolBarHelper is one such class. But really, it is just a helper class that interacts with the framework JToolBar class allowing components to interact with the administrator toolbar.
The framework classes are all found under /libraries/joomla. The application classes are found in other directories.
Ian