If you look at the First Amendment of the United States Constitution, you'll see if that the First Amendment is Freedom of Speech. Now what is more liberal than the right to speak freely and add to that the constitutional right to speak freely. That is what liberalism is really based on. Freedom of speech and assembly, the right for the individual to live freely. Liberal and liberty go so well together which is why they sound similar because liberal is based off of liberty. Liberty for the individual, not liberty for government to manage the individual's lives.
If you look at this whole debate about Bill Maher and his opinions on religion and Islam in general and keep in mind Bill Maher is a real Atheist, you'll know who the real Liberals are and the people who just call themselves Liberals and who the media calls Liberals. Because the Liberals in this debate and I'm one of them are defending free speech and Bill Maher's right to free speak freely. And not be censored because political correctness fascists and perhaps some Muslims as well are offended about what Maher has to say about a non-Christian or Jewish religion.
The free speech aspect is just one example of the Liberal vs. the non-Liberal on the Left in America. The Liberals wants everyone the entire country to have freedom over their own lives. Not just people born to money or from the South or from rural America or who are Christian or who are Anglo. But everyone including the groups I just mentioned that tend to be Republican. The non-Liberal the statist on the Left wants government to have the power to manage our lives for us. Because he or she believes we are too stupid to make our decisions for ourselves.
When it comes to the Left whether it is the center-left or the rest of the Left, it is about role of government. And the same thing on the Right, but on the Left the further you go, the more government especially Federal Government you want both economically and even to a certain extent socially. And if you are on the far-left, you want a hell of a lot of government to manage people's lives for them. But if you are on the center-left where I am, it is not small government you advocate for. But a limited government that is not so big that it discourages individual freedom, responsibility and initiative. Just big enough to do for us what we need it to including helping people in need help themselves.