I've heard these terms used seemingly interchangeably, so I'm a little unclear. Please cite examples.
Unlike Game Engines Game Frameworks make you code a lot. But it's a very good idea to use Game Framework if you want to practice coding. And if you're experienced enough, you can bring together different tools and libraries (or create your own ones) and make something like Game Engine, from Game Framework.
Unity is a 2D/3D engine and framework that gives you a system for designing game or app scenes for 2D, 2.5D and 3D.
In general, a framework is a real or conceptual structure intended to serve as a support or guide for the building of something that expands the structure into something useful.
In computer programming, an engine is a program that performs a core or essential function for other programs. Engines are used in operating systems, subsystems or application programs to coordinate the overall operation of other programs.
These terms, and others, do seem very similar. They're named from a conceptual standpoint, and so could be defined as follows:
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