Probably the big difference is that an engine is supposed to combine several aspects of a game internally. So there will be some kind of core and memory management that pull the strings behind the scene and make different areas work together (user input, sound, graphics, physics ect.).

A framework on the other hand, mostly just provides a set of self-contained functions and classes that help you develop your application while keeping dependencies low.

Quite often there isn't a difference, it depends who you're talking to. There isn't really a single accepted definition of either term; The PopCap Framework for example meets most people's definitions of an engine, and it's not uncommon to see people develop engines that match kiome's definition of a framework.