Socialism is a bit of a rubber-concept. You could use socialism in a broad general sense meaning a system that takes care of its poor, but almost all western societies except the US has a public health care system for example. If that is what the progressives mean, we Scandinavians are socialists, but so are the Brits, the French, the Canadians etc.
And then it can be a system where you have collective ownership of the means of production. Like communism. We are not that kind of system. We are still a capitalist system.
I think that the US discussion has been a little off when it come to what socialism actually is since McCarthy or maybe even before that.