The fabrics do differ from WalMart to your local quilt shop. The griege (pronounced 'grey') goods (the base fabric) has more threads per inch, and is usually the same amount of threads in the warp & weft. This not only makes the fabric somewhat stronger, but I've been told that it's much easier to hand quilt when it's "square". (I don't hand quilt, so can't say from my own experience)
Then again, this may only make a difference if you are looking to make an heirloom quilt. I've personally used fabric from WalMart, JoAnn's, local quilt shops, online shops....and no one has even told me that their quilt came apart! As long as your workmanship is the best you can do, you can use any fabrics you like. Look at some of the very OLD quilts - many are made from fabric that has already been used in clothing, and worn & washed uncounted times, and THEN made into a quilt...that may still be on a bed today! :D