First you've got Marx and his economic theory. I suggest you read it along with the communist manifesto. I don't agree with all of it nor do I think at all his idea of the inevitable revolution of the proletariat is at all in line with reality, but it's a very influential work in economic theory and has driven revolution in the 20th century and beyond, you do yourself no favors by not familiarizing yourself with it as most Americans are anemic to do following a very successful propoganda campaign in the 1950's and later.

The entire issue is essentially too broad and complicated to distill perfectly into a cliff notes version but I'll attempt to hit the main differences.

Marxism essentially postulates that materialism, as opposed to spiritualism, is the primary motivating force in society. And that the materialistic nature of society is organized according to the economic class hierarchy. Rather than by racial or religious affiliations. While a king may claim his right to rule is derived by god, in reality his right to rule is derived from his ability to collect taxes and pay off those under him who protect him and maintain his authority through the threat of force. This is somewhat applicable to most historical societies however Marx ideas are very much referring to the new post industrial revolution society where capitalists were essentially usurping the positions of power from the previously noble and royal classes to become the new upper class.

Communism on the other hand is derived from Marxism, as Marx was certainly party to writing the Communist manifesto. However communism it self does seek the ultimate dismantling of the capitalistic system with the ultimate dictatorship of the proletariat as it's ultimate goal, this is very much an unrealistic and quite unachievable ideal that has never been attempted successfully. Apart from Marxism where we can say it describes the class distribution and economic dynamics of modern post industrial society (or at least it did at the time of Marx) and fairly points out that the ultimate source of economic power does lie with the proletariat, those at the bottom who provide labor, for the benefit of the bourgeoisie, the middle and upper class urban elite who are able to understand and mange labor without producing any material benefit themselves, full on communist ideology calls for the abolishment of this system and is more utopian rather than discriptive in nature.

Maoism, Lenism, Castroism, Stalinism, Ho Chi-Minh Vietnamese Communism, Juche, all refer to various leaders interpretations of Marxism used by revolutionary leaders as they applied it to their own country, all deviate from pure communist theory as they cannot exist outside the economic reality of life, and as such become preyed by many of the same problems and corruption that exist in the capitalistic system, namely the human desire for power at it's core, covered most eloquently by famous socialist author Orwell.

Maoism specifically was driven by students that had become increasingly discouraged at the republican Chinese government and called upon their dissent to totally and utterly wreak havok on any traditional Chinese cultural elements or institutions, with almost religious fever towards the ultimate raising of the self over the culture in a reversal of traditional Chinese cultural paradigm, viewing this from the purely Marxist lense, it served as Mao's vehicle for the deconstruction of the existing power structures, which naturally he replaced with his own, and a new ruling class of communist emerged after tossing out the previous capitalist ruling class, and the new ruling class of communists then became capitalists as they are now. Thereby failing to really be communist in it's pure form. Despite taking the trappings and language of the communists.

How it's similar to the modern situation in the west has to do with the college students total disdain and constant attacks of any and all institutions and traditional beliefs as evil. It is very similar to cultural revolutionary attitudes in post revolution China.

One of the more humorous anecdotes of that time.

https://www.theguardian.com/world/2016/aug/25/china-traffic-lights-red-guards-communism-great-leap

Replace making posters with posting on Twitter and changing the word bousgeoisie to MAGA or BLM and you'd be forgiven for believing that article was describing modern western culture.