Not all left ideas come from the Soviet or communist China although they participated to the experiments. Most socialist parties in EU split from USSR and communist China from the revolutions or when the economical catastrophes (Chinese famines) or atrocities (military repression of opposition and gulags) they committed were revealed. From then, it split between social democrats and communists, social democrats are simply called socialists in those countries (at least France and Spain).
Apart from Sanders, I think American democrats are very far from European social democrats, they rather correspond to our traditional right, which indeed doesn’t care much about rising inequalities. I think the median people live better in European social democrat countries than they ever did in communist countries.