There are no generic batches, but the way they manage their releases and the sheer breadth of product they are distributing does take some work to stay on top of.
The core Bourbon and Rye expressions use a linear and straight forward batch numbering format, although once in awhile you will see a derivative batch that ends in b (e.g., Batch 8b). That apparently happened more earlier, when some of the blended batches sat in a barrel for longer than expected and developed a different flavor profile than the original batch number. I haven't see one of those in awhile. You can read about each of the core batch releases at https://www.barrellbourbon.com/bourbon and https://www.barrellbourbon.com/rye.
Beyond those, they have the Craft Spirits line (15 year old and very expensive), experimental stuff (Dovetail, Armida, Seagrass, Infinity, etc.), a barrel pick program (usually has a weird alpha numeric batch like DSX1), and the new Private Release bourbon (micro blended releases using KY/TN/IN distillate of varying ages and percentages). I haven't tried the Private Release stuff yet, as I need to dial back on buying for a minute to right size my collection.
I'd suggest sticking to the core Bourbon releases unless you really seek out things that are unique and different to the point of not necessarily reading like a traditional bourbon or rye. 25 and 26 were the first batches that used a wheated bourbon as part of the blend, and everyone I have share those with has come away a big fan.