They're soc-dems, which is generally the best approach: democracy as usual with a comprehensive social safety net and progressive taxation.
Social democracy is socialism. The main thing distinguishing it is that social democracy chose to work democratically rather than through revolution. That's why it's called "democratic socialism".
The difference matters. It's kinda like the difference between an attenuated vaccine and straight up shooting someone up with Ebola. Technically, same animal. Realistically, one is more likely to wreck everything because it's too brute-force to have anything to oppose it.
Kinda the strength of democracy - you have people who'll yell at you if you try to starve a couple million citizens, be it on purpose or by incompetence.
I agree, the difference matters. But it's the difference between democratic and revolutionary ideology. Not between social democracy and socialism.
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Theoretically, yes. In practice, though, you're never going to have a completely socialist state under a democratic system for the same reason that no
other ideological strain will be able to establish and maintain the sort of state it desires.
In practice, democratic socialism results in a more moderate state than revolutionary socialism because there are opposition parties and government won't necessarily be formed by a socialist party or coalition in every election. And that's in multiparty parliamentary systems that allow the governing party pretty substantial leeway--in a system like that of the U.S. where minority parties can still block legislation, it's functionally impossible for the majority party to get everything they want, and you've got much greater room for internal dissent alongside that.
Which is why social democracy is nice, as noted above: you generally get a lot of the good points of socialism without the fallout of a revolution or the potential to backslide into authoritarianism.