Bad Bloods aren't just some interchangable concept. The Bad Blood Predator was a Predator Serial killer. He went on a rampage killing whatever got in his way without any of the rules at play at all. He was still a Predator though.
The Supers are very clearly a different breed. Aside of a few pieces of similar tech, they look nothing like Jungle, City, Lost Tribe, the AVP or the AVP R Predators. Their head shapes and details are completely different. They are the wolves to the dogs.