For me, a library is a collection of classes that do useful things. Typically something, that can be useful in a lot of projects. Is that also the case in terms of objective-c? What exactly is a library there? Only classes that have methods? Or also collections of functions? And do they have to be compiled to be called a "library"? Where is the segregation between an "Framework"? Aren't bove the same thing?
Assuming you are talking about a library that uses the Cocoa frameworks and not just one written in the plain old Objective-C language, a library (or framework) is a collection of classes that work together to perform a specific task. I would not organize an ObjC framework as a collection of functions since that totally goes against the paradigm of the language.
As for the difference between a library and framework, that's probably a bit subjective. To me, a library (in the context of your question) is something written in C that probably more closely resembles a non-OO collection of functions. A framework would be a full package of classes as I described above. So the Messaging framework on CocoaDev would be a framework, whereas the sqlite3 APIs you can access on the iPhone would be a library. Again, that's just me. Other people may interpret the terms differently.
According to Wikipedia: "Frameworks are functionally similar to shared libraries, a compiled object that can be dynamically loaded into a program's address space at runtime, but frameworks add associated resources, header files, and documentation."
A framework is essentially a shared library (binary, similar to a DLL) in a bundle that also includes all of the information needed to use that library (like header files, documentation, internationalization resources, etc). A framework without all of the extras is just a library.
There is no requirement that a framework be object-oriented in nature, though I assume that's the norm with Cocoa.
For Cocoa, the concept of a framework generally replaces (enhances) the concept of a library. However, the Objective-C toolchain imposes no such requirement. You can use source-only "libraries" or unix-style binary libraries (e.g. an .so file). I think of a "library" in these generic terms... it's just a collection of useful code, in source or binary form. A framework, on the other hand, is a specific thing with a specific meaning for OS X.