Fascism is charachterized by authority being excercized by the personal politcal will of the persons in charge, not on the basis of adminstrative procedures, laws and set policies. Hence, we see the emergence of a supreme leader, such as Hitler of Mussolini, and the authority of their underlings is derived from his authority, which they usually wield in the same manner as their superiors, not upon the basis of laws, codes, procedures and policies of the administrative aparatus of government.
How the state comes into being is irrelevant to the nature of the fascist state when it is manifested.
Indeed, theie can be fascist acts inside the context of a non-fascist system. As I outlined above, Kenny's temporarily succesful attempt to bar Galloway, basically on his personal authority alone as minister of immigration, was a fascist act, even though, for the most part the immigration department is not a fascist institution.... yet.
Extrajudicial executions of persons on the authority of the president of the United States are fascist.
On the other hand, despite its authoritarian tendencies the Chinese government is not really fascist, since it operates on the basis of a fairly well defined legal code and adminstrative system with set policies, even though it is quite brutal -- it is more of an oligarchy of an elite class, managed by committees that have clearly defined powers and responsibilities.