I've considered Libraries to be the pieces of code that let us 'paper over browser inconsistencies' to be things like jQuery. Sure, they also gave us some useful tools and plugins to accomplish tasks, but on the core purpose was to be able to write simple javascript code for common functions and have parity across all the major browsers.
Frameworks, I view at as code organization and paradigm tools. They create a more consistent structure for a group of developers to work on a single project. It aids in creating an MV* or other similar paradigm that a team can work within. Even outside of a team environment, Frameworks give you a ... framework, of how your app should be built, rather than just creating your own structure as you go along.
This is the reason why there are so many frameworks vs. libraries. Once you've chosen a library to handle browser inconsistency, as the author mentioned, barely an issue anymore, there is an endless possibility as to how your app should be structured. Some people like two-way data binding, some don't. Some people need extreme DOM performance of leveraging the virtual DOM, others hate the idea of having their html closely bound to their javascript (and framework as often the case).