At its simplest, a bag wraps you with insulation, including underneath where the insulation is flattened and not doing much insulating. A quilt is just that, an insulated blanket that goes on top, with a sleeping pad beneath.

In this day and age "quilts" are seldom simple bedding and more typically "top bags" that dispense with insulation directly underneath, but still wrap around the feet and legs to ward off drafts, usually incorporating sleeves or straps to hold the pad in place. At this point there are many variations, maybe start with Big Agnes for a few
models.

Cheers,