Framework is an infrastructure, ready-made and predefined, with some particular rules of the game on the "development field", according to which, you can build your application, on top of it, by "playing with framework rules" (you can, at some extent, customize those rules).
Spring MVC is a good example of Framework. You don't control how the View Resolving, Dispatching or Template Rendering happen and achieve a goal together.
Think of this as a big machine, where you can plug in and integrate your components which are applicable to that machine.
Library, on the other hand, is just a set of classes, which provide already implemented functionality out of the box, in order to not start inventing the bicycle again and again.
Apache Commons is a good example of the Library. It has a lot of ready tools and functionality to facilitate your work with String objects.
Think of this as a set of instruments and tools, using which, you can build your own machine.
With respect to how it is implemented question. This is like asking how the Boeing A220 is built?. I'm not sure anyone can describe here how the Framework is implemented in the details. But if I understood uour point about whether the Framework is used via classes, then:
Framework might provide some classes as an abstraction, yes, but it's not about them, it's more about mechanics of the entire system. The main thing it provides is the mechanism and mechanics of how the system is designed to work.