What liberalism and socialism Classical as well as Democratic Socialism have in common, is that they are both progressive. Meaning liberals and socialists both believe in making society better and the peoples lives in society better. And using government to make society and peoples lives better. But thats about where they have in common ends, as well as liberals tend to be liberal also on Social Freedom as well as Economic Freedom. And tend to be Liberal Internationalists on Foreign Policy. Socialists who aren't communists or a another form of authoritarian, tend to be liberal on Social Issues as well but tend to be dovish on Foreign Policy, as well as National Security and Law Enforcement. Liberals however tend to be liberal on these issues, they are liberal after all and tend to believe that Individual Liberty has to be defended and we don't have a choice but we have to defend Individual Liberty. And that means having enough security to accomplish this without interfering with our Constitutional Rights. Liberalism tends to put its faith in liberty and Individual Liberty not the State, the State is their to protect our Individual Liberty and help people who are down help themselves. Liberalism is about the Individual not the State, socialism at least on Economic Policy is about the State. Using government to make the lives of people better with a whole menu on Social Insurance programs meaning the Welfare State. Liberalism is individualist, socialism is statists and collectivist, that we are in it together as a society and they we need to go forward together or not at all. Even if some people in society can move forward on their own without the government showing them the way.
When Conservative Historians take a look at liberalism and what exactly it means, like in this video. They tend to mix up liberalism with socialism, classical as well as democratic. Whether they do it intentionally or don't know any better and they point to the New Deal era of the 1930s, as well as the Great Society era of the 1960s. These were both progressive era's, where Progressive Democrats in the Federal Government attempted to make America better with a whole wide range of Federal Social Insurance programs. And they created the American Welfare State and I believe had some success in making America better in that. But these weren't Liberal Progressive Democrats who accomplished this, a lot of these people especially in the Southern Caucus in Congress. Were very conservative on Social Issues including Civil Rights. These Progressive Democrats were Democratic Socialists that of course believe that the government meaning the Federal Government, should be used to make society better with the Welfare State.
I don't believe there's been a Liberal Era in American Politics at least not in the 20th Century and definitely not now. Just look at the Obama Administration's positions on National Security and the War on Drugs to use as examples. I believe the closest thing America has seen to a Liberal Era, was in the 1960s. But that had more to do with Social Issues and running against the establishment in society and Social Liberation and Foreign Policy to a certain extent as well.