The left uses the word "fascist" for the NSDAP in order to stir up indignation
Leftists like to use the term "fascist" to refer to anyone farther right than a moderate, but if they could, they would shift the frame to include anyone who is not leftist.
They started by using the term "fascist" to refer to National Socialists, who were not fascists at all. Tom Wolfe explains:
This first American Writers' Congress was held in 1935 . It was an attempt by the Communist Party to remove the red glare in the coloring of their cultural movement--in the arts, movies, literature--and to focus on the anti-Nazi, anti-fascist cause.
In fact, it was the Communist Party that invented the word fascist to apply to the Nazis. The fascists were only in Italy, members of a socialist party known as the Fascisti. The word was never used in Germany. The Communists wanted to obscure the fact that the Nazis and the Fascisti were, like themselves, national socialists. The acronym NAZI stands for the National Socialist Workers Party. So, was Soviet communism national socialism? Absolutely. Communists the world over never did a thing that wasn't for the defense or the advance of the Soviet Union. -- Tom Wolfe, Interview 2006