I don't know which WalMart Schwinn you're looking at, this one
is the only Schwinn road bike I found . I gather you're also looking at the cheapest of the LeTours
First and foremost, the WalBike comes in only one size, 55cm. If 55cm is not your size, you'll be uncomfortable, sore and could damage your joints.
Second, bear in mind that WalBikes are pretty much designed to be purchased, ridden once or twice, then stuffed in the back of the garage and forgotten. Thus, the components don't need much longevity. If it lasts a couple of hundred miles, its done its job. So there's a huge quality difference.
The LBS bike's components, while low-end, will still last several thousand miles. The components on the LeTour are not that far off from those on my entry-level bike which turned-over 5,000 happy miles this week. While I upgraded the wheels and tires, and have replaced worn chains and brake pads, I haven't had to throw anything out and start over. (EDIT: The saddle. I replaced the saddle too.) I expect many more thousands of happy miles on my entry-level bike.
Third, the LBS bike comes fully assembled, properly
assembled, and most have a lifetime free tuneups policy. It's just the labor on adjustments, but that's worth something. It should also come fitted to you.
Fourth, 32 pounds for the WalBike. That's a ton in road bike terms. While unspecified, the LBS Schwinn will be lighter. It should probably have better welds too.
Fifth, shifters. The WalBike uses stem-mounted friction shifters. While some people--mainly retrogrouches--prefer them, most people these days prefer the integrated levers found on the LBS bike. They put the shifting and the brakes right at your fingertips while riding. This is probably represents the single largest price difference between the two bikes. Shimano charges dearly for their integrated levers.
Now a finer point.
The WalBike's a 7-speed double compared to an 8-speed triple. Fewer gears to choose from and bigger jumps between them when riding.
That's a start.
EDIT: At the LBS you'll be able to test ride the bike--or bikes--before you buy. Even if you don't really know what you're doing, it can still go a long way towards selecting the right bike and building confidence in your purchase.
Remember size matters--a lot. There's more to it than standing over the bike to be sure is doesn't crush your dangly bits. Only a test ride can help you determine if the bike fits while you're on it and in motion. That's where the bike fit counts--not while standing around on it.