Definitions of fascism has always been problematic because it is a chimera. Personally I really like this one: Fascism is the moral belief in inequality based on identity, like e.g. ethnicity or gender. It is a bit more wide ranging definition, but pretty simple and clear. For example a democracy where women are not allowed to vote and are exploited as cheap labor at home would be fascist.
Contrast that with neoliberalism, which is the moral belief in inequality based on class / wealth. Which explains why they ally so easily.
Check out the book I linked. The definition of fascism is an academic question.