You can have piecework without quilting (fancy Victorian coverlets made entirely of velvets/satins and the like- commonly embroidered and usually with the patches cut in no particular shape- are called 'Crazy quilts' and are almost never actually quilted), (I have seen photos of them made from silk cigar bands and patriotic commemorative ribbons, too)

you can have precisely cut geometric patches which are then sewn together and quilted (what most people think of for the the word 'quilt'),

you can have appliqued pieces of fabric sewn on a base fabric and quilted,

you can have *folded* pieces of fabric with other pieces insert and covered by the fold, and then stitched together, usually without quilting (Cathedral Windows 'quilt' is the one I think of, but there could be more),

You can have *reverse applique* quilts, traditionally made by small tribes/island people in South America, in which solid color fabrics are layered, cut through, and stitched down with small blanket stitches sometimes in contrasting colors, to reveal underlaying colors- the quilting on these is generally 'contour' quilting, in large, bold stitches of many different colors,

The variety of textile techniques that are gathered under the idea 'quilt' is huge. There's many more.