I have made a few quillows. Mine are all regular quilts with an attached pocket that the quilt folds into. My DH asked me to make a lap quillow with the pocket quilted too, so he could put his chilly toes into the pocket when he is reading.
While every quilt show has a definition of a quilt, they are not always the same. My view is that unless you are showing the quillow, it's up to you what you call it.