You mean mass surveillance, massive propaganda (very similar in style, although that could have been a 30s/ 40s thing) and suppressing the opposition (the first ones to go into KZs were from the political opposition)? Not to forget benefits for party members.Its commonly believed that because the Nazi's has 'Socialist' in its name, that it was a Socialist party. It wasn't. There are, however many commonalities between the Far Left, and Far Right. I wouldn't go as far as subscribing to the horseshoe theory though.
Back in the days (after the Weimar republic collapsed) of the rivalry between the communists/ socialists and the NSDAP, there were clashes between their fighting "forces", with the SA a bit more organised (uniforms) and some people say that a lot of the communists just swapped sides and joined the SA.
Which, strangely, happened again after the Third Reich collapsed and some NSDAP supporters (especially in the industrial sector) were all of a sudden squeaky clean democrats and the GESTAPO became the BND and Verfassungsschutz, with the kind support of the CIA.
This also happened after the German reunification when the ex SED members, STASI officers and their informants, quickly "integrated" into the Western political system.
And now Germany turns into a totalitarian, oppressive state (again), while wearing the mask of a democracy. And with Antifa the SA is back in a different appearance (brown became black) but with the same purpose, to beat down the opposition without having to fear prosecution.