They are both very diverse political philosophies and take libertarianism to use as an example. Where the basic idea of libertarianism is that you combine personal with economic freedom as long as individuals aren’t hurting innocent people with what they are doing. But that government is there to protect us from invaders, terrorists and criminals. Thats the basic idea of libertarianism. But then there’s also anarcho-libertarianism, which is borderline anarchism if not anarchism all together. Where Anarcho-Libertarians basically have no role for government in society. And are even interested in privatizing things like prisons, fire departments and law enforcement to use as examples.
Socialism, another diverse political philosophy where you have Socialist-Libertarians like Noam Chomsky. Socialist-Liberals like Ralph Nader and people with this philosophy believe in personal freedom like Libertarians, but that government needs to be there to sure that economic wealth is distributed equally in society and where no one is rich, or poor. But then there are Socialists who are statist across the board and not only want to prevent people from becoming what they would call too wealthy and not poor at all.
But that government also has a role to protect people from getting hurt and even protecting us from ourselves. And making bad decisions with their own lives. Like prohibition, which is definitely a progressive idea. The whole junk food and soft drinks ban, the War on Drugs to use as examples, are all progressive ideas. And people like this I would call Progressive-Socialists, or Progressive-Paternalists. People who are socialist on economic policy, but also Statist on some key personal choice issues.
Progressive-Paternalists, want to use government to control what people can eat, drink and smoke to use as examples. You also have Marxists-Socialists, people who believe in eliminating capitalism and the private sector all together. Where the government would own the economy all around on behalf of the people. And then you have Socialists who believe in both capitalism, but that is highly regulated and taxed to finance a large welfare state. So with Libertarians we would get a lot less government in society. And with Socialists a lot more government especially as it relates to the economy.