Liberals and progressives aren't necessarily allies, neither are they necessarily enemies.

Liberalism is... broad. Super broad, actually. I'm going to break up Liberalism, therefore, into classic liberalism - namely, the concepts of freedoms - civil rights, freedom of religion, secular governments, etc, and social liberalism - which is where the comparison to progressives is stronger.

A classical liberal holds a political stance that would likely be in favor of hate speech, or even (to take the example to an extreme), something like a call to violence, because in their view, the ability to express oneself, so long as it doesn't actively deal violence, would likely be acceptable.

A social liberal holds a political stance that would be against these things, because of the inequity present, behind the concept that the good of the community needs to be in a balance with the good of the individual. It's under this reasoning that they would, for instance, want to restrict the right to bear arms - it is in their argument that the community as a whole is being adversely affected by the ease of access to firearms. (A point complicated by the fact that studies about that particular topic have been banned in the United States, which makes it arguably, without scientific support, a social liberalism cause that is not a progressive cause.) Social liberals came about in the US around the 1880s, under the - and this is where it gets confusing - umbrella of the Progressive party.

Now, this said, the Progressive ideas from above? That's why they're tied into liberalism so closely in the US. There's also been a lot of language drift regarding 'liberal' in the US - particularly in the last 30 years - which has led to progressivism holding more of its original ideology within the modern context of its word, which is one of the reasons you see it used more often to describe a social liberal stance.

This is why I stated I'm talking about the Progressive ideals at the start of the last post - because the Progressives are also a political party founded by social liberals. Progressivism at its whole (away from the party's platform) isn't so much a tightly-defined political philosophy as it is a generic call to action based on the empirical evidence, knowledge, and reason, to use these tools to help the betterment of mankind. As an overarching philosophy, it could be most directly compared to the overarching philosophy of conservatism, in that progressivism believes we must change, and that the onward march of progress is inevitable, often sudden, and ultimately beneficial, and conservatism believes that change should be resisted completely, or very slowly acquiesced at all, in an appeal to tradition and the current status quo.

Conservatism these days often doesn't actually look like that, but again, you rarely hear liberals talking about their inherent rights to personal freedoms despite societal backlash, either. This is what I'm talking about when I describe 'language drifting'

It's in this way that Progressivism (a concept predating social liberalism by a couple hundred years) gets credit for social liberals. It may help to imagine that Progressivism in this case is a rectangle, and social liberals are a square. Social liberals are simply one type of Progressive - the type that pursues social goals. Another type of progressive would be the technological progressive, a modern example of which would be Elon Musk, who believes that we inexorably must march forward, and apply logic and reason to the betterment of society - but isn't particularly known for being politically oriented in nature.

Does this help clear things up?