Yes, to get back to the question:
I think they are almost precisely the same.
It comes down to the nature of progressivism, as an ideology, and on the left an extremely common one. Some people might argue it's inherent in leftist ideology; I don't think I necessarily agree with it, but it has often been the dominant perspective, which is why they tend towards utopianism.
Marxism, of course, takes for granted a kind of progress in history, and sees it as playing out through class struggle.Leftist identity politics substitute various identity groups for class categories. But the end in both cases is a kind of utopian society, an end to history. It absolutely sees history as having a telos.
It's a common idea that Marx essentially inherited this idea of progress from Christianity. The only reason we might intuit it is if we see ourselves as being all round more enlightened than those in the past (as we will, because that is our bias.,) and of course all of history has led to where we are now. SO it can appear as if there is some movement toward a more enlightened end - but it's an illusion.
What's interesting is that Christianity, at least in orthodox forms, makes no claims about this happening as a strictly historical process. On the contrary, it seeks to explain the evident impossibility of an end to history, and the solution to that, while it takes in history, or intersects with it, is not and cannot be historical. God is seen as being outside of time and history, and as underpinning what is true and real, so in a sense could be said to underpin any true ideological position.
Marx, being a materialist, took that and reduced it to a material, historical movement, but there seems to be no real justification for the idea that there is an end to which it is all moving. But to my mind that is where this idea of the right side of history comes from.