Today, social democracy mostly agrees with social liberals and neoliberals that nationalization should be used very rarely and sparingly - mostly wrt. inherently-monopolistic "platform"-like businesses such as railways, power grids or telco infrastructure. And even then, these "platforms" should be open for multiple private competitors to operate on, as opposed to providing monopolistic services of their own via vertical integration.
“Some social concerns” is really brushing over a lot of the things that make social democracy a form of socialism.
You’re missing for example that in a social democracy it’s common for private companies affiliated with what you could call “public service” to be in part owned by the state.
These companies most often used to be wholly state owned, but through the market liberal agenda many things have been sold out. Sometimes for better, sometimes for worse.
A lot of what is considered welfare is also not necessarily privatized.
I could go on, but instead I suggest diving down in the topic through the supplied wikipedia link. https://en.m.wikipedia.org/wiki/Types_of_socialism
Here you’ll find social democracy, liberal socialism and democratic socialism described in detail - all part of the value spectrum of socialism.
Also, getting flagged for this opinion seems a bit over the top...