 This talk will be about exploring the differences between generic group models. Generic groups have been used extensively to analyze the possibility of new cryptographic assumptions, to prove black box impossibilities, and sometimes to justify the security of crypto systems built from groups. Given their importance, it is crucial to understand these models. The literature contains two generic group models. The first on the left is Schuess model, which uses random labels to represent group elements. The second generic group model is Maurer's model, which uses handles. I like to think of Maurer's model as imposing a strong type system, dictating that the only way an algorithm can manipulate a group element is by a group multiplication and testing equality. No other operations are allowed. These two models are often treated as equivalent. However, the purpose of this work is to explore how they are in fact quite different. This may be surprising, but it was already present either implicitly or explicitly in several prior works. However, the exact relationship and the implications of their differences was never really explored. This work explores the relationship more thoroughly. The high-level takeaway is that Schuess model, when in doubt, is the model to use. The reason is that we find that Maurer's model fails to capture many generic techniques. To the point where many classic textbook results do not hold in Maurer's model, despite easily holding in general groups. Schuess model, on the other hand, does not suffer from these limitations. With that said, there are some cases where Maurer's and Schuess model can be used interchangeably, which will be elaborated on in the full talk. As a bonus, along the way, we also have something to say about the algebraic group model, which has recently received a lot of attention. Please see the full talk for details.