I think you're a bit confused. Marx in no way stated that Capitalism was Feudalism, in fact much of Capital is focused on the specific characteristics of Capitalism, and how it emerged. Both Feudalism and Capitalism are class societies, but these aren't the same in any stretch. Moreover, the Bourgeoisie largely emerged from merchants who through primative accumulation managed to gather the seed Capital to build up industry and bring about Capitalism, and thus overthrow the aristocracy and Feudal lords. The Bourgeoisie overthrew the aristocracy, some aristocrats fell into the Bourgeoisie, but the Bourgeoisie emerged and overtook them as a class.

You are correct that both Capitalism and Feudalism are class societies, but you're entirely off the mark on the Marxist interpretation of them. I think reading Capital would be good for your understanding if you want to be a Marxist about it.

This is a bit pedantic, but Marxism has never been about equal wealth. Marx actually rails against "equalitarians" in Critique of the Gotha Programme:

The right of the producers is proportional to the labour they supply; the equality consists in the fact that measurement is made with an equal standard, labour. But one man is superior to another physically or mentally and so supplies more labour in the same time, or can work for a longer time; and labour, to serve as a measure, must be defined by its duration or intensity, otherwise it ceases to be a standard of measurement. This equal right is an unequal right for unequal labour. It recognizes no class differences, because everyone is only a worker like everyone else; but it tacitly recognizes unequal individual endowment and thus productive capacity of the worker as natural privileges. It is, therefore, a right ot inequality, in its content, like every right. Right by its very nature can consist only in the application of an equal standard; but unequal individuals (and they would not be different individuals if they were not unequal) are measurable only by the same standard in so far as they are brought under the same point of view, are taken from one definite side only, for instance, in the present case, are regarded only as workers, and nothing more is seen in them, everything else being ignored. Further, one worker is married, another not; one has more children than another, and so on and so forth. Thus, with an equal performance of labour, and hence an equal share in the social consumption fund, one will in fact receive more than another, one will be richer than another, and so on. To avoid all these defects, right instead of being equal would have to be unequal.

Unequal needs with equal pay results in unequal outcomes, hence "from each according to their ability, to each according to their needs."

All in all, the problem with classifying social programs as "Socialist" or "Capitalist" doesn't really mean anything, because what matters is the overall context of the system. This is the purpose of Marx's Dialectical Materialism, rather than judging discrete elements, it must be judged in context. Social programs like healthcare in the Nordic countries are not "Socialist," they are funded through Imperialism and exist to limit revolutionary pressure, as these safety nets came about via proximity to the USSR which provided similar or greater safety nets. I'm being pedantic, admittedly, but because I am trying to espouse the importance of taking a consistent stance among Socialists, chiefly Marxists as I myself am a Marxist-Leninist.