Can someone illustrate what really is the difference between the two?
Even though they are two very different things, one can argue they both solve a software architecture problem
a design pattern solves many software architecture issues (about creation, behavior, concurrency, ...) with different pre-defined design. (design being an implementation of an architecture topic)
a framework is based on the Hollywood Principle ("Don't call us, we call you"), where you implement some high level requirements as specified, and leave the framework do the rest of the work, calling your implementations.
A key difference is the scope cohesion:
design pattern have a tight scope:
framework has a large scope:
For instance, .NET is a framework composed of: