I find it extremely annoying when people say they believe in Evolution but can't even identify which theory/hypothesis of evolution they claim to believe and most people have no clue that there are several theories of evolution
I find it annoying, although completely understandable, when people misunderstand what "theory" means in scientific practice (including when would-be stalwart defenders of The Scientific Method myth, whose knowledge of scientific practice is limited to textbook descriptions that scientific organizations such as the National Academy of Sciences and the AAAS have fought against, declare that in the sciences something that is "theory" isn't "just a theory" but something akin to fact). The "theory of evolution" is an incredibly successful, incredibly broad framework for understanding everything from the dynamics of empirical investigations into changes between individual generations of fruit flies, the entirety of evolutionary psychology, numerous fields within computer science, particular approaches to understanding the most fundamental questions within cosmology and theoretical physics, and of course practically all biological sciences. Theories are frameworks and/or models wherein particular phenomena and/or processes of particular types are explained, expanded, interpreted, tested, and understood via components of these frameworks, the application of logic, and empirical findings. Evolutionary theory is so broad a framework entire sciences (like evolutionary psychology) are founded upon it. It is not reducible to any singular proposition, statement, or description but is, like fields of science more generally, singular at its core whilst details of particular phenomena that it describes and explains can be more open to disagreement as can interpretations of more general aspects of the theory. This is often true of theories, though seldom are they as successful or as broad as evolutionary theory. In quantum mechanics, for instance (perhaps the most successful scientific theory ever), what exactly the theory even IS and what it entails has been a matter of extreme debate since its inception.
The differing terms you use do not describe different theories of evolution, but differing processes and components of evolutionary theory. These are neither as distinct nor as incompatible as say, gravitation in general relativity, quantum mechanics, and particle physics (or as classical vs. embodied theories of cognition or even approaches to biology, such as relational biology as compared to computational).
Because of evolutionary theory's enormous success at explaining such diverse phenomena and as a tool more generally, naturally we find not only different processes at play within the framework but also differing opinions about particular details. This doesn't involve different theories anymore than the fact that e.g., there have been several decades over the temporal vs. rate neural code, the independence of difference quantum field theories, the diverse number of generative linguistic models (e.g., the classic TGG, government & binding, principles & parameters, and minimalism), and so forth, somehow entail differing theories. In fact, in each case mentioned the differences are in fact less than the so-called differing "theories" of evolution you list.
