It’s hard to talk about a specific non-Leninist Marxism because much of Marx’s, as well as Engels’, works were not published until long after their deaths. A lot of the concepts associated with Marxism in fact came out of Russia Marxism which would later develop into Marxism-Leninism.
The terms “dialectical materialism” and “historical materialism” which is usually treated as one of the most fundamental philosophical aspects of Marxian philosophy was not a term Marx ever used but in fact coined by the Georgi Plekhanov, a Russian Marxist and Bolshevik.
One of the most important works for dialectical materialism is Engels’ book Dialectics of Nature, and one of the most important work for historical materialism is Marx’s book A Critique of the German Ideology. Neither of these books, in fact, were ever published until the Marx-Engels institute of the Soviet Union collected the notes and published them, which was of course many decades after the deaths of Marx and Engels.
This means that despite non-Leninist Marxism being, on paper, just Marxism without Leninism, it has trouble escaping from its Russian Marxist roots and tends to still carry a lot of the ideas intrinsic to Marxism-Leninism at its core. Most will still accept the ideas of dialectical and historical materialism, which is at the root of Marxism-Leninism and Russian Marxism in general, and so their core philosophical basis are in fact identical.
There are some non-Leninist Marxists who do try to disagree with this basis, some criticize dialectical materialism due to it largely being associated with Engels’ writings and not Marx’s. But overall it’s pretty much a small minority point of view for a Marxist who is not a Marxist-Leninist these days to reject the philosophical basis.
Usually what separates Marxists from Marxist-Leninists is more of a disagreement over economics and politics and not something different at a foundational level to the philosophy.
Marx argues that capitalism is based on competition, and competition is based on decentralization, but capitalism has a tendency to replace competition with monopoly, and thus to replace decentralization with centralization. Not all in one stroke, but very very gradually, slowly but surely, over long periods of time, enterprises get bigger and bigger and the economy becomes more and more concentrated.
Marx saw this as unsustainable because the very basis for the capitalist system destroys itself over time, but also didn’t think it was possible to roll back the clock and return to an era where everything is operated by very tiny small enterprises. So he thought eventually a change to the political system would need to occur that would transform the laws and institutions to be inline with these large centralized enterprises rather than antagonistic to them, i.e. to make them public property, i.e. socialism.
This inevitably means that for Marx, it was most likely that socialism would come out of the most highly developed capitalist countries first, it would come out of the countries with the largest and biggest enterprises.
Marxian economist Rudolf Hilferding would argue in his book Finance Capital that he believed it would be possible, contrary to Marx, for a poor country to introduce a sort of pseudo-socialism because the rise of finance capital made it very easy for a state to centralize control over the heights of the economy without having to nationalize small businesses, they would become nationalized “indirectly” because they all rely on these centralized commanding heights of the economy. So the economy would not be fully publicly owned or planned but it would be effectively socialist because the public sector would play an enormous leading role in the economy and every non-public enterprise would be dependent on them.
Hilferding thought that the imperialist capitalist system which was used by rich countries to pillage poor countries could in fact be used as the conditions for breaking free of capitalism, as it spreads finance capital to these countries which are a tool the workers there can seize to build this pseudo-socialist system.
Hilferding was incredibly inspirational to Lenin and his book Imperialism: The Highest Stage of Capitalism, and Lenin would go on to repeat similar a analysis inspired by Hilfreding as well as John Hobson’s Imperialism: A Study and argue that the countries that are under the boot of the imperialist system are the “weakest link” in the global chain of capitalism and thus the most likely to break free from it.
Hence, Marxism-Leninism adds a lot of economic ideas on top of classical Marxism and thus reaches a very different conclusion from Marx: successful worker revolutions are likely to occur in poor countries under the global imperialist capitalist system first, not the wealthiest capitalist countries.
Leninism also adds some political ideas as well. Such as, democratic centralism in the party, which was introduced as a tool to try and unify many different competing Marxist factions in Russia at the time. It basically argues that the party should allow criticism and debate, but once the votes have been cast and a solution is final, it is binding on all members.
Leninism also introduces the idea of a “vanguard party.” Just because you have a brain and can use it, doesn’t mean you are immediately an expert on neuroscience. In a similar sense, Lenin did not believe a person simply being born in a capitalist system was sufficient to fully understand it, and class consciousness required academic study.
So Lenin introduced a sort of meritocratic hierarchy. The Communist Party is not a party, for Lenin, was not simply a general mass party for anyone to join, but is a party that should have standards and only allow entry of dedicated workers who actually are committed to the cause, and people who climb the latter to the top of the party should be people who are merited and have studied Marxian theory and have shown their ability in practice.
In order words, the “vanguard party” is less of a mass party for everyone to incorporate all the workers, but a party of the most politically active, educated, and experienced workers that has the task of leading the workers.
Lenin was a big critic of what he called “tailism” which was when mass parties would simply follow whatever protest or event was popular among the people at any given time, when Lenin argued the party instead should be the ones playing a leadership role. They should be the ones starting protests, starting rebellions, promoting slogans, etc. That’s what being a “vanguard” means, that the party is always ahead of the curb, trying to lead the masses in the right direction, rather than just tailing wherever they are already going.
A lot of non-Leninists hate the idea of a vanguard party and either reject parties altogether or think the party should be a mass party that just follows the people wherever they go and does not try to influence or lead them, or maybe something else entirely.
It’s usually these economic and political differences that non-Leninist Marxists criticize Marxism-Leninism from, and not foundational philosophical differences.