The "condescending saviors" being referred to were the utopian socialists. The utopians would be those like the followers of Owen, Cabet, Fourier, etc. where these writers would basically come up with visions of what an egalitarian society would look like and then, based on these designs, they'd go off and start their own projects/towns/cities/whatever. In a nutshell, the idea was that everyone would see how wonderful the communities were and then decide to do that instead of capitalism. Its also referring to the followers of people like Babeuf or Blanqui who thought the revolution should be carried out by a small group of people basically staging a coup and then using the power of the state to bring about socialism.

Marx, on the other hand, sees the necessity of class struggle to overthrow capitalism and bring about socialism. In the Theses on Feuerbach, which Davis talks about in this section, Marx argues that people are shaped by the world, by their circumstances, but at the same time people also shape and change these circumstances - and therefore also themselves - through the activities they engage in. Learning through doing. So, rather than socialism being brought about by some dude theorising about it, Marx says that it will be brought about by the self-emancipation of the working class. Its basically the whole "The philosophers have only interpreted the world, the point is to change it" thing. The working class are exploited by capital, they will inevitably look to resist their own exploitation, and the ultimate emancipation from this exploitation lays in the abolition of private property.

As for differences between Marx and Lenin with regards to organisation: As far as I understand it, Marx's view of the party was essentially that communist associations were to be formed all around the capitalist world which the radicalised members of the working class would join. The workers would then elect representatives who would attend an international congress where problems and suggestions would be discussed and then a formal program would be agreed upon. This would be overseen by and the program carried out by a central committee who were answerable to the congress. For Lenin in What is to be Done, he doesn't see an open party or democratic structure as a workable possibility in Tsarist Russia as it would be too easily infiltrated by spies and supressed by the police. Instead, as you mentioned, he proposes a smaller, secretive group of professional, experienced revolutionaries who would advise and direct a broader and more informal base. Basically, Marx's ideas focused more on a bottom-up kind of organisation, whereas Lenin focused more on a top-down kind of organisation. Or that's my interpretation of things anyway.