A comforter is usually filled with synthetic fiber filler. The filler is stitched to the comforter with usually patterns on it. When you need to wash it, you need to put the whole comforter to your washer. If your washer is too small for your comforter, you would need to take the comforter to dry clean.
A duvet is usually made by more expensive down feather and it needs to be used with a duvet cover.
A duvet cover is a protective cover that has a long opening (for example, a zipper) so you can insert your feather duvet to this cover. A duvet cover is washable and will protect the duvet from stains, damage, and dirt.
In other words, a duvet cover is like a pillow case that protects the pillow. When you want to change the look of your bedding, you can just purchase another duvet cover and replace the old duvet cover with the new duvet cover by opening the zipper on the end.