What is the difference between a framework and a library?

Actually these terms can mean a lot of different things depending the context they are used.

For example, on Mac OS X frameworks are just libraries, packed into a bundle. Within the bundle you will find an actual dynamic library (libWhatever.dylib). The difference between a bare library and the framework on Mac is that a framework can contain multiple different versions of the library. It can contain extra resources (images, localized strings, XML data files, UI objects, etc.) and unless the framework is released to public, it usually contains the necessary .h files you need to use the library.

Thus you have everything within a single package you need to use the library in your application (a C/C++/Objective-C library without .h files is pretty useless, unless you write them yourself according to some library documentation), instead of a bunch of files to move around (a Mac bundle is just a directory on the Unix level, but the UI treats it like a single file, pretty much like you have JAR files in Java and when you click it, you usually don't see what's inside, unless you explicitly select to show the content).

Wikipedia calls framework a "buzzword". It defines a software framework as

A software framework is a re-usable design for a software system (or subsystem). A software framework may include support programs, code libraries, a scripting language, or other software to help develop and glue together the different components of a software project. Various parts of the framework may be exposed through an API..

So I'd say a library is just that, "a library". It is a collection of objects/functions/methods (depending on your language) and your application "links" against it and thus can use the objects/functions/methods. It is basically a file containing re-usable code that can usually be shared among multiple applications (you don't have to write the same code over and over again).

A framework can be everything you use in application development. It can be a library, a collection of many libraries, a collection of scripts, or any piece of software you need to create your application. Framework is just a very vague term.

Here's an article about some guy regarding the topic "Library vs. Framework". I personally think this article is highly arguable. It's not wrong what he's saying there, however, he's just picking out one of the multiple definitions of framework and compares that to the classic definition of library. E.g. he says you need a framework for sub-classing. Really? I can have an object defined in a library, I can link against it, and sub-class it in my code. I don't see how I need a "framework" for that. In some way he rather explains how the term framework is used nowadays. It's just a hyped word, as I said before. Some companies release just a normal library (in any sense of a classical library) and call it a "framework" because it sounds more fancy.

A library performs specific, well-defined operations.

A framework is a skeleton where the application defines the "meat" of the operation by filling out the skeleton. The skeleton still has code to link up the parts but the most important work is done by the application.

Examples of libraries: Network protocols, compression, image manipulation, string utilities, regular expression evaluation, math. Operations are self-contained.

Examples of frameworks: Web application system, Plug-in manager, GUI system. The framework defines the concept but the application defines the fundamental functionality that end-users care about.