I think our socialists over here in the U.K would be very different to yours. so I'll just say that and shut up and read other peoples posts to get informed-

I believe the Democratic Socialist Movement in the U.S. is primarily defined by and promoting a social welfare agenda. They want universal, low-cost or free healthcare which covers pre-existing health conditions for ALL U.S. citizens. Plus, many are proponents of free college tuition for at least the first 2 yr of college, a la Bernie Sanders. They do tend to favor federal gov't interventions over states or individual "rights" or gov't for the most part. This is not necessarily a bad idea, IMO. There is definitely at least a slight difference between socialism and communism, which are often considered interchangeable in the USA. I believe that Dem Socialists are normally on the side of reasonable restrictions on guns and gun control, as well. The way I see it, extreme liberalism inevitably leads to some form of socialism. They are basically flip sides of the same coin. Hope this helps you.

One thing I don't think anyone has mentioned is "who controls the marketplace?" In the US we have gotten to the point where corporations totally control it. They write their own regulations. They police themselves. Executives are the cabinet members, watchdogs, and CEOs. The only people who matter to a corporation are shareholders and immediate profits. In my idea of a socialist leaning government, there is a regulation of the marketplace to protect consumers, the environment, and labor. That along with the education, health care, and social safety net issues.

Good question...

I went to answer, then realized all my trails lead outside the USA.

I wouldn’t claim to know a lot about it, but I think the system would have to vary from country to country. I think American socialism revolves around universal health care, free college tuition, and a more equitable distribution of wealth along with more investment in infrastructure and education and less military spending.
Honestly, I have no idea what I’m talking about and I’m really just avoiding exercising and going to the grocery.

Welcome - I wish I could rattle of a definition, but I would say the most common democratic socialism is that of Bernie Sanders group