I think socialism by definition forbids private ownership of capital. So countries that allow for private capital (which is most countries) are not socialist. North Korea does not allow private ownership of capital, so they certainly qualify as purely socialist. I believe Laos is similar. Same with Cuba.
China is interesting in that they used to be socialist, and have since transitioned in recent decades to a sort of state capitalism. There are still heavy restrictions on private capital in that you can own it, provided it's in partnership with the state (to some extent). See Jack Ma and his issues with Ali Baba as an example.
Just swapping the two terms around does not mean the same thing. "Democratic socialism" is socialism. "Social democracy" is still capitalistic with an expanded role of the state. Go educate yourself.
The people who got most of the UK social programs started in the 1900s called themselves democratic socialists, not social democrats. I am not sure when the terminology you are describing was introduced, but it is not universal.
