The skull collectibles from both NECA and Sideshow illustrate that they have distinct and significant biological differences. Their skull structure is different, they have unique heads, feet, and dreadlock placements. They logically must be a sub-species, ala Feral being another type of sub-species.
Personally I've always made the comparison between Homo Sapian and Neanderthal. Both are part of the Hominidae family yet all the other early humanoid species died out. That apparently didn't happen with the Predators.
I'm not hung up on the naming thing personally, and I find the 'Berserker' and 'Super Predator' names to be interchangeable. But given their description in the scripts as these self experimented on, juiced up Predators with black blood... no the movie didn't follow that idea, thankfully. Though the next one sure did.
They were also referred to as a Super Predator clan in AVP Evolution, and I think they are referred to as that in the BTS materials of Predators post when that draft was. Those probably helped to contribute to the name sticking.