Here's some ancient history: Until the 1970s, everyone in the UK slept covered by a thin sheet (usually cotton but occasionally [yuck] nylon), then some woollen blankets, and in winter you put a feather-filled quilt on top of that. The outer layer of this, often silk, was part of the quilting and therefore fixed. These things were virtually unwashable. Eiderdown was a more old-fashioned word for these. Then, at about the same time as we discovered yogurt, pasta and "real" (as opposed to instant) coffee, the "continental quilt" arrived. That's the object you describe, with the washable cover. "Duvet" - the French word for "down" - was an alternative name that caught on a bit later. In answer to your question, yes, I guess a duvet could be called a quilt - especially by people too young to remember what a quilt was before duvets arrived. But a quilt (with a fixed cover) , either the old-fashioned silk type or the patchwork handicraft type, can never be called a duvet. I hope that makes sense.

The item in the picture is usually called a duvet in the UK, but 'quilt' is used sometimes. Try searching on a UK online shopping site, for example Amazon. You will see that, although the product descriptions sometimes use both words, the product packaging almost always uses the word 'Duvet'.

They are interchangeable but "duvet" is more modern and more common now. We might use "quilt" more often when it has been home-made. "Quilting" is still a hobby.