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In regards to why Americans refer to social democratic parties as socialists, it has a lot to do with Americans just not knowing what socialism is.

A lot of the Cold War propaganda portrayed communism/socialism as being defined by an over-arching, authoritarian government. So this idea of communism/socialism being defined by the amount of government involvement eventually turned into there being a divide between the communism of the USSR/People's Republic of China and the "socialism" of the Nordic countries (even though this is actually social democracy) in the minds of the American people. The reason for this being that since the government has a lot of involvement in the economy and social safety nets they must be socialist because no "true" capitalist government would be that involved.

This sort of thinking is still pretty influential, in the United States, today. Many high school and college textbooks (particularly McGraw-Hill's "Understanding Business" textbook) will reinforce this "communism vs. socialism" divide, where they'll define socialism as being something along the lines of "an economic system based on the idea that some basic businesses should be owned by the government so that profits can be more evenly distributed among the people" while defining communism as being something along the lines of "an economic system where the government makes most of the economic decisions and owns most of the means of production".

Another aspect of this is that because of the McCarthy trials, the terms "communist" and"socialist" became bad words, leading to those words being used as insults (usually by American conservatives) against anybody that wants to have more government involvement. So since social democrat parties advocate for more government involvement than your average neoliberal, American conservative deems necessary, they're stereotyped as being "socialists", and unfortunately, the classification has stuck.