Social democracy and democratic socialism were historically one movement. The first social democratic party in Europe was Marxist. "Social democracy" and "democratic socialism" are pretty much used interchangeably in Europe. Nordic model social democracy traces back to Eduard Bernstein's vision of social democracy, which did not entail abolishing private property. On the other hand, Fabian socialists called themselves social democrats, and they did want to abolish private property. Nevertheless, the practical proposals of both factions were almost identical, in spite of the theoretical differences. So there was never a split. The distinction between social democracy and democratic socialism is not really made by the proponents themselves. Personally, I do make that distinction for practical purposes, but the terms are largely used interchangeably by people that adhere to either.

I won't delve into the taxation thing, since many of my posts already address that.