“Socialism” means different things to different people. But in general, when people in the US say “socialist,” they mean to conjure up associations with Soviet communism, one of the worst dictatorships in the history of the world.
However, in much of Europe, and the rest of the world for that matter, socialism isn’t a “bad word” — it’s just a term for a political philosophy involving a significant amount of state efforts to reduce poverty, reduce economic inequality, etc.
In France, Spain and Portugal, for example, the left-of-center parties, which in most cases are not much more to the left than the Democrats in the US, are all called the Socialist Party. In other countries they are called Labor (UK, Israel) or Social Democratic (Germany, Norway), but these parties all tend to be members of the Socialist International (the moderate Socialist international organization of left-of-center political parties).
Since the founding of Marxist communism, democratic Socialist parties have always distanced themselves from Marxism and Soviet communism, and had vastly different policies. That said, some Democratic socialists have often had some interest in Marxist philosophy, and for that reason are more likely to be atheists. However, since the 19th century, and continuing today, there have been socialists who are inspired by religious and humanitarian motives rather than Marxist philosophy. In fact, this kind of socialism actually predates Marx and Marxism. (Marx hated those “reformist” socialists!) Today, in Israel, all the religious parties are more left-wing on economic matters than the Democrats in the US.
Personally, I don’t like the word socialism, because it is suggestive of the authoritarian politics that killed tens of millions of people in the USSR and China in the 20th century, and because it denotes a more extreme outlook.
“Social democratic” is a nicer term, I think, because the only connotations are with countries such as Germany or Netherlands or Denmark, which despite having some economic troubles at times, have always been peaceful and orderly places with the rule of law and civil freedoms. Interestingly, in some aspects the most “socialist” of these countries are actually more economically free than less socialist countries — it’s easier to hire and fire workers, for example, in the Scandinavian countries than it is in the more meager and underdeveloped welfare states of Southern Europe.