Maybe I can offer some help here. There really are only 2 major players in the battery world in the USA. They would be East Penn Manufacturing in Reading, PA and Exide Battery Co.
Several years ago, I had a Deka battery that was in a vehicle that lasted about 7 years. When it died, I wanted another Deka. So I went on the hunt to find them in RI. Well, one thing led to another and I ended up at East Penn Manufacturing in Reading, talking to some one in Production. He told me that the Deka brand was not in my area or town, and asked me if I had a Benny's Home and Auto store near me. I said yes, about a mile away. He said the Benny's brand( Guardian ) is the same battery.
He then went on to talk about all the batteries that they make for private labeling that go to Walmart, Advance, Napa etc. etc.
The Die Hard battery is not a Sears product, but rather a branded battery. So the bottom line here is that you could go into any number of stores, and come out with the same battery, but just a different label. If somebody sells Die Hard batteries, they just bought the rights to the name
The important thing here is to match OEM size and CCA characteristics and not buy an upsized super duty battery that will not get the proper exercise. Been there and done that. Sears was big on upselling and they got me years ago. Bottom line, they die quicker.
Hope this helps. Questions?? I would call east Penn Manufacturing and ask them whose brands they produce currently.