Follow-up question: What exactly is the difference between "liberal" in the US and in Europe? OP describes some differences, but I'm still a bit puzzled. Thanks!

I wrote out a very long answer last night and lost it to a computer crash, so I'll try to give a shorter one here, and if it's unacceptable I defer to the moderators.

While the base form of Liberalism that came about in the 17th and 18th century focused on the personal liberties and the idea of popular sovereignty, unique factors in American history changed how this manifested.

While before, Liberal ideals resulted in suffrage, equal protection under law, taxation representation (think Britain's 1689 bill of rights) and therefore lower taxes, etc., the issue of slavery in America's Civil War had to answer tough questions about liberty. While many people had liberty to purse their life/liberty/happiness, others did not. There was not equal suffrage, equal protection under the law, and other discrepancies depending on who you were.

As a result, you see a shift in Liberalism focusing on a government protecting liberty/freedom, to the idea of government creating circumstances ensuring liberty and freedom for a wider range of people instead of favoring a few. You can see this in a lot of the traditional liberal thinkers changing their attitudes to fit this ideal. Writers like John Stuart Mill, Thomas Hill Green, Lester Ward, and even Thomas Paine often went on "socialist" bents at one time or another later in their careers (though Ward was pretty heavily already socialist but you get the idea). So as a result of this social liberalism favoring a larger government to push for equal liberties, you start seeing the term "liberal" used more to describe a left-of-spectrum idea while "conservatives" tended to prefer the older idea that the liberties of some will override that of others whether by chance or action, and yes sometimes because of factors like ethnocentrism depending on the individual who you are talking to.

It wasn't until roughly the 1980s that Liberal became mostly a purely Democratic Party thing after shifts in the Republican parties in the 1930s and 1960s. Even as late as the Nixon era, ideas like affirmative action and the Environmental Protection Agency were coming out of Republican politicians, while both of those come under threat of disenfranchisement or dismantlement by modern conservative Republicans.

A caveat is that your Liberals aren't likely as right-leaning as many of our right-leaning politicians are. Even Liberals in places like England or Canada would be described as kind of middling to left-of-center to slightly right in terms of balance of beliefs here in the USA (I have a personal grudge against the whole idea of a centrist or moderate in political science conversations but I could write a book on that).

Sorry for a less-detailed answer, but I really didn't want to re-write that post.