This is what I've picked up through osmosis
Socialism is:
a) What they have in Nordic countries/Europe. The "kinder communism"
b) OR actually just as bad as regular communism, what they have in Venezuela/USSR/Cuba. Extremely evil, no freedoms, no 34 different brands of toilet paper, awful. All socialist countries are dictatorships.
These two contradictory definitions somehow simultaneously exist in many people's minds.
Communism is: unquestionably bad. No private property at all, you can't even own a hairbrush. Everything is the same, drab and dreary. Bread lines. Somehow more extreme than Socialism despite commonly being thought of as the exact same thing.
Marxism is: the most extreme form of communism ever. The big bad. Somehow worse than both communism and socialism combined despite being the same thing as them. Some Americans will insist that actually socialism is good because that's what they have in places like Denmark and Bernie said he was a socialist, but MARXISM is bad because that's what they had in the USSR. Associated heavily with the destruction of western values and bringing about horrible things like LGBT rights and abstract art (???)
Anarchism is: a violent, completely free-for-all way of life. Mostly just 17 year old larpers. Destruction for destruction's sake. The exact opposite of communism on their rudimentary political compass, but also somehow part of the left at the same time.
In fairness, the US left has had to rebuild itself and learn over 100 years of history and unlearn cold war thinking. As for the rest of America, yeah thats even more work.
Cold war propaganda fucking ruined the minds of basically all Americans lmao. Even old black radicals have become overcome with lib brainworms. Most of the western left are trots. Tbh, the US is in a better position than most of Europe because our left was destroyed and is being rebuilt while theirs continued to exist but was pushed to the sidelines to devolve into crankery. British MLs are crank terfs, the rest are crank trots. Also, ironically the fact that we have large racialized underclasses means our left isn't plagued as badly by chauvinism as the European left is.