I am reading a book that mentioned the post war leader of fhe East German communist party was a socialist prior to becoming a Marxist. It's hard for me to imagine a socialist who wasn't influenced by Marx because he is so deeply intermeshed with modern socialist thinking (at least from my outsider perspective---I am not a socialisy myself just interested in the history of it).
What distinguished Marxist socialism from non-marxist socialism or pre-marxist socialism?
Well, that doesn't make a lot of sense since while there was socialism pre-Marx, Walter Ulbricht was member of the left.wing of the German Social Democratic party under Luxemburg and Liebknecht, both would classify as rather Marxist Communists of the Council Communist variety.
Don't get me wrong, there is non-Marxian socialism such as Autonomism, Mutualism, and Anarcho-syndicalism but Ulbircht is firmly embedded in the Marxist tradition of socialism.
Perhaps your confusion arises from the different terminology in terms of Socialism and Marxism: Socialism in the broadest sense refers to a society in which the means of production are socialised and is generally seen as a way to Communism, i.e. a society in which property of the means of production ceased to be altogether and thus the state, money and class cease to exist altogether. Now, in a socialist society of whatever variety, semblance of the old order still remains.
The question of Marxian vs. non-Marxian ways of socialism often refers to the role of the state in the period of transition from capitalist to communist society, several prominent brands of Marxist-socialism such Marxist Leninism placing the state in lieu of the community owning the means of production.
While Ulbricht was a council communist, i.e. a form of socialim in which the means of production are controlled by councils, and not a Marxist Leninist, this is not incompatable with Marxist theories.
The term socialism was published when Marx was a child and used long before he was born, of course the core ideas of the term had been around for several decades previous and arguably as far back as specialized societies.
Socialism pre Marx is largely the same in practice as socialism post Marx which is not in any way to discredit his influence or genius but mostly Marx turned what had long been sentiment into academic form. Early socialist ideals are the same ones of today but defined perhaps by a focus on smaller groups, many of the early socialists (Robert Owen as an example) might be compared to syndicalists, they wanted the workers to own their workplace and be the sole beneficiaries of it and they wanted small communities to function on this basis as communal societies in rejection of liberal individualism.
A notable exception and perhaps the first socialist is Henri de Saint-Simon who advocated for utopian societies on a larger scale, his idea of governance is quite different where the government was simply there to ensure people were not preying off the system (and was not phased out) and he did not advocate class conflict nearly a much as Marx but otherwise the ideas are very similar, workers deserve what they produce being the central keystone and a rejection of an idle class that does not labor for it's income.
Full disclosure in advance, I am a socialist.
This will be rather short, excuse me for that. Other posters have already touched upon the actual question you asked. But I think I can clear up some confusion about what you mentioned about that book.
Walter Ulbricht was a member of the Social Democratic Party of Germany in the 1910s. In modern Germany they are like any other social democratic party, back then they were mostly democratic socialists. Their previous name (until 1890) reflects that - social democratic workers party of Germany. Ulbricht was part of the left wing in the party though. That's the party wing that split off after the war, first forming the USPD and then the KPD (communist party of Germany).
He joined the KPD in the early twenties. So I think what the author of your book tried to convey was that Ulbricht started politics as a socialist in the SPD and then became an important figure in the Marxist- communistic KPD after the war.
There was a form of Socialist thought prior to Marx, which he, along with Friedrich Engels, coined as "Utopian Socialism," to contrast with the Marx and Engels interpretation of Socialism, which they coined as "Scientific Socialism."
In short, the difference between the two classes of socialism is that the Utopian Socialists believed that it was possible to achieve a perfect society without any revolution, and that it was possible to achieve a utopia without violence, or very little, which sharply contrasts with Marx's Theory of Historical Materialism, which distinctly states a revolution is necessary to switch from the Capitalist to the Socialist mode of production.
Engels wrote Socialism: Utopian and Scientific which pretty clearly outlines the difference between the two competing socialist ideologies at the time of Marx.