I think they got democratic socialism confused with social democracy (which is understandable given the similar names). The difference is that democratic socialism is... well, socialism and that social democracy is just liberalism with a social safety net.

(Side-note: Socialism is in essence about organizing the economy democratically so the fact that tankies have coopted the term to also mean totalitarian state capitalism unless democratic is added as a prefix is such a shame.)

Edit: apparently I have it backwards actually, disregard

You may be confused by the term you're using, taken separately the definitions of the words feel as though they should mean what you intend them to mean but together they are used to refer to capitalism with restrictions which always inevitably leads to wealth inequality as capital takes indirect and then direct control of the government.

The socdem system is temporarily great for the people living within it but unfortunately it cannot survive without the exploitation of people outside of the country. This is commonly seen in the global south as corporations exploit cheap labor to keep prices low in their primary retail countries usually in the west. This is literally a form of imperialism.

Now I might have just explained all this to someone who is already well aware and if that's the case I apologize.

Anyway the term you are looking for is socialist democracy. It's dumb that democratic socialism doesn't mean what it sounds like it should mean but unfortunately it doesn't.