Post 1933, the Nazis were fascists. Prior to 1933, they were socialists.
In 1933, following Hitler's rise to the top of German government, Hitler ordered the assassination of all the top socialist leaders in the Nazi Party ... i.e. The Germans of WWII that everyone thinks of when they hear the term Nazis were fascists, not socialists. Hitler's fascists hunted and killed socialists and communists among others ... like the Jews.
Political Parties change over time ... For example, Unlike today, the Republican Party in Lincoln's day was predominantly a liberal party while the Democratic Party was predominantly conservative. And, prior to the passage of the Civil Rights Act in 1964, Southern blacks voted Republican while Southern whites voted Democrat ... the opposite of what we see today.
You should do more reading on this subject.
Here's a video on fascism from a series produced by a History teacher ("HipHughes History" found on YouTube)
and a few "articles" to consider:
https://www.youtube.com/watch?v=tQlMtoDp8ks&t=5s
http://www.historyonthenet.com/chronology/timelinenazigermany.htm
http://isj.org.uk/divided-they-fell-the-german-left-and-the-rise-of-hitler/
http://www.rense.com/general37/fascism.htm