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.
I guess the one good thing about the US' view of the left is that being a Marxist here actually means something, unlike Europe where parties that can't even be called social-democratic anymore claim the heritage of Marx.