If Socialism is Capitalism with more regulations, is the United States Socialist too? It has plenty of regulations, more than Social Democracies do in many areas, in fact. Are you going to tell me that every country is actually Socialist if it doesn’t have a laissez Faire Capitalist economy, even if it uses Capitalism as the primary mode of production?
You want a source? Marx’s Capital. Read it, you might learn something, even if accidentally.
Social Democracy absolutely takes influence from Marxism, that’s perhaps what the source you list may be referring to, however the place where Social Democrats fight with Socialists on is Social Democrats believe Capitalism can be harnessed and benefited from, instead of needing to transition to a worker owned economy.
I am not confusing Capitalism with markets, again, Wikipedia defines Market Socialism as a market based economy of competing worker-owned entities. Your own source, against you! Ha.
Similarly, I am not confusing Socialism with Communism. Communism is a Post-Socialist society, one that is Stateless, Classless, and Moneyless. Communism is indeed one form of Socialism, as is Syndicalism, as is Anarchism, as is Council Communism, as is Market Socialism.