unless your name happens to be Bob LaFollette, I don't think the progressives of today are espousing the progressive policies of the early 1900s, any more than Democrats of today are espousing the bimetallism of William Jennings Bryan.
Fair enough. But if progressive and liberal policies coincided in the past and don't coincide today, that, too, is evidence that the two concepts are distinct.
But independent of whether I'm right on this particular aspect, I'd like to pursue your idea that progressives are intimidated liberals who dare not speak their name anymore. I agree with that. And I think it matters, because I think it's bad strategy to change one's brand in response to detractors disparaging it.
For example, take the historical cat-and-mouse game about the proper name for the African-American community ("We're negroes". "No, we're Black." "No, we're Afro-Americans". "No, we're people of color --- not to be confused with colored people", etc). Compare it with the gay community's strategy of owning swear-words like "fag" and "queer" and turning them into badges of pride. In my opinion, the gay community's strategy worked far better, and left-of-center Americans ought to emulate it.