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@trwnh No, not always.
For instance, let's say a podcast makes a post about their new episode. I loved the episode so I want to share it to my followers.
I could just boost if, but instead I "quote post", adding: "whoa, great new episode of this podcast. I've you've ever been curious to check the show out this would be a good one to start with."
I would not consider that a "response" because it's not addressing the original poster
@trwnh I don't think there's any one answer to this
One of the most common use cases is commentary or response, a "loud reply" as @erincandescent put it. I think most of the hostile uses of quote posting fall into this category (which is not to say it's always or even usually hostile)
But also sometimes it's just to add emphasis, explanation, or even just personalization to a "boost." i.e., to share something with an explanation of why you're sharing
@trwnh I would say the "the post being quoted" is embedded content within the "quote post", exactly like media or a link preview.
In all of those examples, the post is usually presumed to be "about" the content it's referencing. "Check this image/link/post out. here's what I've got to say about it."
Which makes it odd (to me) that the content being commented on is usually displayed below the text of the post. If I were designing from scratch I'd do the opposite.