In case you were wondering what "Marxism" might be other than a Republican swear word ...

This may only be of interest to political theory geeks. Ramsin Canon published a good discussion a couple of years ago of a framework for understanding historical Marxism from today's perspective. (What It Means to Be a Marxist Jacobin 12/11/2018)

But because Marxism has a massive worldwide history extending back to at least 1848, the year the Communist Manifesto was published, it has had many variations. Most of which would define the other Marxist trends as not truly Marxist, or faulty brands of Marxism.

And of course those who reject Marxism with various degrees of passion have their own versions of what the "Marxism" they reject is. At the moment in the US, it's become fairly common for Republicans to refer to even moderate Democratic candidates who wouldn't hink of calling themselves Marxists as socialists, Communists, Marxists, and radicals. And ones that adhere to QAnon conspiracy theories have even wilder accusations.

Jacobin identifies its mission as "offering socialist perspectives on politics, economics, and culture." In contemporary terms, I would say they fall into a left-social-democratic spectrum.

Canon's broad framework is this:

Marx himself famously once said that he himself was “not a Marxist” if certain askew interpretations of his theories of historical materialism and capitalism were “Marxist.” Part of the problem is that the theories and processes that Marx helped create are too big to fall under a single -ism; Marx was a philosopher (and sort of historian) of political economy, that is, the study of production and trade in relationship to laws, customs, and human systems, whose theories helped inform numerous other disciplines and practices: economics, sociology, history, literature, and practical politics, among others.

The closest analogy that I can think of is to what we would today call “Darwinism,” the theories of nineteenth-century biologist Charles Darwin. Darwin didn’t invent biology, paleontology, genetics, or any of the numerous disciplines and practices that are informed by “Darwinism.” And in fact, there are many aspects of classical “Darwinism” — the theories and conclusions arrived at by Darwin and his immediate disciples — that have been outright revised or rejected by people who today would still consider themselves “Darwinists.” Since Darwin published On the Origin of Species and The Descent of Man, hundreds if not thousands of scientists and philosophers have expanded on and improved Darwin’s theories (the so-called “modern synthesis”) — obviously a necessity since during Darwin’s lifetime there was no deep concept of molecular genetics. [my emphasis in bold]

Canon's article does contain a technical mistake. He discusses the very controversial notion of the "dictatorship of the proletariat," and his brief discussion strikes me as a good explanation of how Marx understood the concept. But he writes that the particular phrase, dictatorship of the proletariat, ”comes from the Manifesto and a work called Critique of the Gotha Program."

The phrase does appear in the latter: "Between capitalist and communist society there lies the period of the revolutionary transformation of the one into the other. Corresponding to this is also a political transition period in which the state can be nothing but the revolutionary dictatorship of the proletariat."

But not in the Manifesto itself.

For more on the history of that particular concept after Marx' passing, see: Robert Mayer, The Dictatorship of the Proletariat from Plekhanov to Lenin Studies in East European Thought 45:4, Dec. 1993.

The first chapter of Hal Draper's The "Dictatorship of the Proletariat" from Marx to Lenin (1987) that deals with Marx' own version is available online, The ‘Dictatorship of the Proletariat’ in Marx and Engels Marxists.org.