Not all ammo advertising is designed by folks with a user's background, especially internet mail order places. It makes shopping for some things like 308 W and 45 ACP brass tricky.
That said, some listings are better than others and if you follow the specific part numbers of SKU of ammo or brass, some of the better outfits will tell you the specific primer configuration used on that part number.
Once you find a good web supplier who tells you what size the primer is on a particular 308W case, you then have the part number identity for everywhere else that may not list the difference. Sometimes the word "Palma" brass can imply small primers. In the 45 ACP, it happened that "lead free" indoor practice ammo was noticed by bullseye competitors and they adopted it and added some small amount of the demand for it.
The small primer 308 brass exists for several reasons, most of those reasons were the popularity of the case design and adoption for match shooting. 308 is the parent case for many other designs which also share the demand for a SRP version, for example all the 6 BR variants. The use of the 308 cartridge as a "military" design qualified it for F-T/R and International Palma competition, so there was enough reason to have US and European firms create a small primer version for competitive use.
As time passed and the 300 Meter competitors adopted certain cartridges, many of those were also offered in both small and large primer configurations, so always do your homework and inspect your cases when dealing with brass that has a history of match use with more than one primer size.