That description pretty accurately describes the process I have with my mother.
She quilted for years before I got into it, but her favorite part of the process is hand quilting which she does on a large frame. Having had 3 kids move out of the house, she has plenty of room to set up frame with good light in an unused bedroom. She doesn't really enjoy piecing on a regular basis.
I live in a small apartment and sew in the dining room, have an older, simple machine. I don't enjoy hand quilting and I certainly don't have the room to set up a frame here. I have machine quilted crib-sized quilts and enjoyed that process but don't want to go larger. I tried quilt-as-you-go and did not find it enjoyable. On the other hand, I enjoy designing and piecing quilts on a large, bed-sized scale. Often we collaborate on picking out quilting motifs to complement the piecing - she prefers intricate but not dense hand quilting.
I identify myself as a quilter, but when I describe the process I say that I do the piecing and my mother does the quilting.