In the prophetic taxonomy of the Dead Kennedys' California Über Alles (https://genius.com/Dead-kennedys-california-uber-alles-lyric...), they're 'Zen fascists':

    Zen fascists will control you
    100% natural
    You will jog for the master race
    And always wear the happy face

Though today, they'd be more "fleece/denim secret police".

I think they meant authoritarian, they come in all political stripes

It would more accurately be described as corporate-flavored collectivism.

Of course, that doesn't make for a good ingredient in angry epithets.

Frank Herbert once made the observation that corporate hierarchies were very similar to feudal hierarchies, just with milder consequences for disloyalty and failure. (The hierarchies within organized crime are even closer to the feudal ones, even including the feudal ceremonial trappings. This even works across cultures, where Japanese organized crime harkens back to feudal Japan and Italian/Sicilian organized crime harkens back to medieval and rennaissance Italy.) Along this line of thinking, corporate flavored collectivism should be structurally similar to Stalinist USSR, including the requirement for ideological conformity. However, the branding is likely to be far, far different.

Corporations certainly have purges. Happens all the time after mergers.

Both, this is why the apple bite is shaped like a horseshoe.

"authoritarians"

Fascists and communists are both animated by the same principle: that Papa knows best and must be obeyed.

Fascism and communism are not complete opposites.

Both are authoritarian political philosophies with a heavy handed approach to economic policies.

Differences come in privatization, immigration, equality of rights, and religious toleration. [1]

Both have extreme takes on ideas falling under the umbrella of socialist thought (hence, Germany's National Socialist Workers party). You can argue 1984 vs Brave New World, but there are certainly common themes.

Both differ significantly from classical liberalism.

[1] http://www.differencebetween.net/miscellaneous/politics/ideo...

A friend of mine also pointed out that they appear to have different attitudes towards hierarchy. At least, the Marxist derived authoritarians brand themselves as egalitarian -- though they usually go ahead and have hierarchy anyway, having it both ways. Fascists and Nazis also seem to emphasize community while extolling elites, great men, and meritocratic hierarchy -- also having it both ways. It's just that the branding is different.