Walmart buys it's lead acid batteries from a variety of vendors nationwide, (and worldwide) and the contracts may run for short or long time periods, but generally they will be major manufacturers.
These major vendors also generally have their own logistics network, including rail docks, warehouses, truck fleets, and of course, truck drivers. These trucks are NOT part of the large, highly visible, Walmart fleet.
These vendors also manufacture private label batteries for a variety of retailers like AutoZone, NAPA, O'Reillys, and many others, and those trucks make deliveries at all of these retailers along a route, and of course, pick up the returned batteries to be recycled. This economy of scale helps keep the prices lower.
Pinning it down to one vendor for all of the millions and millions of batteries sold would defy all logic, unless that one vendor can ramp up production to millions of units per day, along with the logistics network, to meet the entire demand of the entire network of stores and clubs worldwide.
And then if that one vendor had any problems in the manufacturing or supply chain, it would mean NO batteries would be available anywhere for awhile.
Sometimes the battery will have a manufacturer's name or code...failing that, its often hard to know for sure.