What do you think the "social" in social democracy stands for if not social-ism, dude.
People appropriate and change the meaning of words all the time. Remember, East Germany was "The German Democratic Republic" and North Korea is "The Democratic People's Republic of Korea" - by that logic they MUST be Democratic, since it says so :/
The socialist economic system isn't compatible with capitalist free market system - social democracy is a hybrid of capitalism, democracy and reformism. Whilst they might approach things from a "social justice" point of view, the reforms under social democracy have nothing to do with socialist economic theories. e.g. you won't find a discussion of the "welfare state" in Marx, Engels, Lenin, Stalin or Mao
Socialism is defined as " social ownership of the
means of production and
co-operative management of the economy". Since true socialist systems stipulate the workers as the owners of the assets, no "welfare" is factored in, because there's no "other" to "hand out" "their stuff" - everyone is employed and their job provides them with a living. Until capitalist reforms, all benefits were provided by Chinese companies to their employees for life as part of their pay - hence there was no welfare system as such.
In social democratic countries, almost everything is owned by autocratic top-down private corporations, or run autocratically (top-down) by bureaucrats, with little input from the people who work for those organizations (worker participation in the management of their own workplace is a key element of socialist economics).
The "means of production" is privately owned, and the government is left to provide all non-producing, but still vital services - the stuff no corporation wants to run. That's not socialism - it's a band-aid on the capitalist system.