Socialism means state control of the means of production (as opposed to control by owners of those assets). That’s actually a definition of “state socialism” but since in practice there is no other kind I think that’s sufficient. The most important means of production today is money.
All modern economies today are hybrids, consisting of some market forces alongside some central control. The argument today is over whether we need more or less central control of the economy; my view is that the way in which the federal government is controlling the economy should be changed. There should be less central control domestically and a lot more central control on international trade or, said another way, what we’ve been doing for the last half century has been almost completely backwards.
The irony of those who are arguing in favor of Scandinavian-style cradle-to-grave welfare systems for the United States is that they don’t really understand the systems in those countries. In general they’re even more capitalistic than we are. However, they are a lot more Lutheran. I do wish such advocates would provide examples that are multi-ethnic, multi-racial, and multi-confessional. That doesn’t describe the Scandinavian countries in any meaningful way at least not when their systems were set up and not until very recently. The closest example I can think of is the Soviet Union.