The difference between Europe and USA comes from WW2. Europe was devastated by the war, impoverished. To avoid revolutions (like Russia), (US-imposed... we can argue about this too) governments on West Europe had to find a mixture between private property and state-owned economy (with the help of US money through the Marshall Plan). This was called Welfare State. The USA did not have war on its home land, so it needed no welfare state, and anyway, McCarthy was there to deter any left-wing thinking/movement into the country, which continues until today.
I would also include countries who are striving to attain Full Communism in the definition of communism.
Even if the representatives resulting from the selection process (which, in pure socialism, is usually a non-democratic process conducted by political elites) were to truly represent the entire population, there may be conflict and a variety of opinions on how to proceed on any given issue. Those who win these conflicts might be called leaders, and they are not engaging in direct democracy.
Direct democracy is one exception to this.
As I said, "socialism" is well defined. If some people like to attribute this "adjective" to their policies/country/whatever that's up to them, not to real socialism meaning.
And in the US, whatever extra pay you get by virtue of having a degree gets eaten up by the loan debts...