This should be a good discussion for me to follow because I'm not sure on what is being asked. Different parts of the country use different terminology, like there can be differences between "piece work" and "patch work" and terms start or change over time.
I mostly know the term "quilt shop quality fabric" in terms of fabric swaps. In which case, yes, most everything your LQS would carry would count. From time to time I have gotten bad pieces of fabric from high quality names so brand name, price, and where bought don't always guarantee whether something is going to pass my feel test. Likewise I've had some lower end fabrics printed on nice greige goods (the raw rolls of fabric) that were absolutely lovely, so again brand names and price aren't the only indicators.
In terms of what makes a fabric more suitable for quilting or other use can involve the weave, which in quilting is usually not textured, even, with a fine equal thread in both directions. Personally, though, I've used various weaves like home spuns, ikats, jacquard, or other non-standard fabrics. Canvas can be 100% cotton but too thick or too coarse a weave to be suitable for quilting.
I tend to like lighter weight fabrics of a smooth even weave, like batiks. When you are used to working with them, a lot of what other quilters feel is prime and desirable can seem rather thick -- or on the other hand, the batiks can feel flimsy to those used to them.