In a word-- yes! 
Higher priced fabric is almost always better fabric.  Read on.   And if you find my guide at all helpful, hit the vote button at the bottom of the page.  :)

The difference:

When people refer to "quilt shop quality" fabrics, what they mean is fabrics that are usually more expensive because they have a higher thread count and are more color-fast.  Just like sheets.  :)

In quilting, a fabric's thread count matters for several reasons.  Like sheets, a higher thread count usually means a softer fabric that wears longer and shrinks considerably less than it's lower thread-count counterparts.   A higher thread count also means your fabric is less likely to beard (allow fibers of your batting to come up through needle holes) when you're quilting it. 

Generally speaking, lower quality cottons are stiffer than higher quality.  And it's not unusual to find very similar prints in chain stores (Hancocks, WalMart, etc) that you would find in your local, or online, quilt shop.  This does not mean it's the same fabric, though! 
Mills will often do a test run on lower quality fabrics to make sure the colors are printing true, that they don't fade and bleed and so on.  Box stores usually get any of these test runs, if they're sold.  They're usually marketed under a different brand name though, so as not to confuse the consumer. 
And then there are the companies that produce cheaper fabrics deliberately in order to meet the price criteria of the chain. 

Does it matter?

Generally speaking, fabrics that you find in big box stores are going to be your lower end fabrics.  This isn't necessarily a bad thing, depending upon what you plan to do with your fabrics.  I love to check the fabric section of Wal-Mart, for example, because they often have cute prints that I really like! 

I carry fabrics in my quilt shop that retail in box stores (VIP & Springs) for that very reason.   Sometimes you just really have to have that fun John Deere print for the curtains in your kitchen and things like thread count and quality don't make any difference in an application like that.  Or you're making your daughter a skirt with Strawberry Shortcake on it.  She'll most likely outgrow it before quality, or the lack thereof, is even an issue.  
 
So, as long as you realize the difference, enjoy the discount!  We can buy more cheap fabrics than we can quality ones.  ;)

But when it comes time to make a quilt--something that is going to take a significant chunk of your time and effort--it's time to upgrade in fabric.  You want something that is going to live long after it goes through the washer a few times.   That initial outlay in cost will be more than made up when you see how many more years your project will survive to be loved and admired.

What names to look for?

Moda (my personal fave!), RJR (Thimbleberries), Alexander Henry, P&B, Henry Glass, Kaufman, Timeless Treasures, Michael Miller, Shamash&Sons, Maywood, South Seas Imports, etc, etc.  Basically, anything that has a retail price over about $7 per yard ($8-10 is common in a shop) is going to be your "quilt shop quality" fabrics.   Unless you shop at online stores, that is.  You'll find many of us who are strictly online can discount a bit more than a traditional brick and mortar store. 

But that's a topic for a whole other guide.  ;)

Summary:

Fabric is one of those things where you truly do get what you pay for. Sometimes cheap is fine, sometimes it's not.  But keep the differences in mind when shopping, and be an educated consumer!  :)