There is unfortunately a lot of confusion about these words. People use the term Socialism to mean "the existence of social programs paid for with taxes" and they also use the term Socialism to mean "a planned economy." This means in practice that "socialism" isn't always the opposite of "capitalism."

Some examples:

• When the government pays for your health care that can be "socialism," but it's not anti-capitalist.
• When the government makes it illegal to own private property that can be "socialism" and it is more or less anti-capitalist.
• When the government raises your taxes to spend more on welfare programs that can be "socialism," but it's not necessarily anti-capitalist.
• When the government makes it illegal to make a profit selling widgets that can be "socialism," and it's explicitly anti-capitalist.

When people say they want to "capitalism is the problem" often what they are really thinking is that the government should provision more services. What they want is universal healthcare or increased spending on other social programs. But that's not in any sense anti-capitalist. That's just taxing economic activity to pay for the social programs you want.

That's what Denmark does.

They are a capitalist country with high taxes that spends a lot on social programs. Some people call that increased spending "socialism," but crucially they still allow markets. You can still be a capitalist in Denmark. Most people there work for private corporations/businesses. Etc, etc.

Some people insist that restricting free markets isn't Socialism, it's Communism, and such people get very upset if you don't use the correct term. But the point is that there is not widespread agreement about how to use these terms and, further, people deliberately deploy these terms in ways that advance their political goals (whether pro- or anti-socialism/capitalism), so it's important always to be clear about what you're saying.