I agree that 'scrap quilt' would suggest it is made from actual scraps. However, I don't think it suggests an unplanned quilt (Bonnie Hunter quilts, for example); I think it would just as likely involve a pattern as a quilt made with just a few fabrics. And I don't think it would necessarily be utilitarian rather than a showpiece, although I do think random (as opposed to color-coordinated) scrap quilts tend to have a homier look.
I think people use 'scrappy' to mean various things. To me (because I don't have a large stash or a well-organized reserve of scraps), 'scrappy' means that I've used a variety of fabrics to represent a single color in the quilt, and that I've most likely bought at least some of them specifically for that quilt.
I think some people use the terms interchangeably, to mean a multi-colored quilt made with many randomly chosen leftover fabrics.