It wouldn't surprise me if it is close to the same product. As an ex-longterm Walmart employee I can tell you that a lot of the products that they put their name on and say "compare to...." are actually just cheaper made versions of whatever they are comparing them to. For example, their diapers are cheaper made knock offs of pampers. It was in a news article they sent out to associates at the time when I worked there, or else I'd find it online and show you myself.
Does that mean that it's exactly the same? No..... not exactly. The ingredients are the same, but the first two ingredients on the product are switched. In Manna Pro pro formula the alfalfa comes first where as in the small world wheat middlings come first. So while it's the same ingredients the order of which they show is the same as with any food. Wheat middlings is more prominent in the Small World where as alfalfa is more prominent in the Manna Pro. Due to keeping industry secrets there's no way to know how much of the formula is wheat middlings, but I'd say there's quite a bit.
I've tried a lot of feeds over the years and settled on Manna Pro. My suggestion would be to try it on the rabbits and see how they do. Do they hold condition? Does their coat stay dense or does it thin out? Depending on how many rabbits you have may make a difference on what you decide. If you only have a couple rabbits, a couple extra bucks buying it at Walmart may not matter to you.
My final answer, no they are not the same. Similar and by the same company, but no