All that’s needed for an audio format is a specification. The features and requirements of that specification may be a subset or a superset of another specification. In this case, compatibility with existing hardware was a requirement for the spec. (Remember that DVD-Audio had some compatibility issues.) But you’re right: just using features doesn’t make a separate format.
I think a more accurate comparison is between CD-ROM and CD-ROM XA (in the Yellow Book standard), or CD and CD+ (in the Red and Blue Book standards). CD-ROM XA and CD+ are both multisession formats, but they organise the sessions in a predictable way, and store specific types of data there in predefined locations. When you don’t have a specification that accounts for special use cases, you get problems with usability or compatibility. Some early game CD-ROMs had CD audio in the same session as the data track. It was possible to play those tracks in a CD player, but the Yellow Book specification made no allowances for this. Since the data track was in the same session, it showed up in the playlist. Playing the data track made a loud, irritating screeching sound that could go on for ages if allowed to.
Problems like that had already been solved by the time Blu-ray was invented. But there was still an unsolved problem left over from the DVD era: How do you make Blu-ray (which was designed for video) usable on a headless sound system? HFPA and Pure Audio took different approaches to this.
HFPA just programmes the menus such that one doesn’t need a screen to choose a stream (7.1, LPCM, etc.). Pure Audio went a step further and colour-coded each audio stream to the red, yellow, green, and blue buttons on the Blu-ray remote. That colour coding is now part of AES-21id-2011, which is the Pure Audio spec. The Blu-ray standard allows content makers to programme the coloured buttons differently on every disc, but Pure Audio makes their behaviour consistent. So, what you have is a minimum standard for how sound is encoded, and how it is accessed.