The question is mostly one of semantics and depends on definition.

Nazism is an example of a group of ultranationalistic militaristic expansionist supremacist ideologies that started taking shape between the 1880s at the earliest and the 1920s at the latest. Other examples include Falangism, Rexism, Hungarism, and... indeed... "Fascism".

In this case, the word Fascism refers to "Italian Fascism", that is to say the ideology of Benito Mussolini and his followers.

HOWEVER, in recognition of the fact that Italian Fascism, German Nazism, Spanish Falangism, Hungarian Hungarism and the others share a broad historical context and ideological base, the word "Fascism" or the term "Generic Fascism" are also used as a term for an ideological family rather than a specific ideology within that family. The choice of term is due to the fact that Italian Fascism was the first example of this category to take power (in 1922) and thus as early as the mid-1920s became a popular term the world over to classify authoritarian nationalistic movements and states.

Sometimes, authors differentiate by using both capital-F Fascism and lower-case-F facism, the former being the Italian subtype and the latter being the family of ideologies.

If you are interested, I can delve deeper into the historiography of fascism and the historical evolution of the term, but in general, the current consensus of historians favors the usage of a generic category of fascism. However, the minority view that disputes the usefulness of the term as a category persists.

/u/Klesk_vs_Xaero has previously answered:

• What were the differences between National Socialism and Fascism?

/u/commiespaceinvader has previously answered:

• What do the early stages of fascism look like, historically?

• Did the Nazi government ever describe their movement as as a form "Fascism", or were Fascism and Nazism conflated by later historians?

• What is Fascism? What beliefs does it entail? (/u/restricteddata also)