Well, you're being selective in your comparison. The part you left out is the part where that other definition continues on to opine about the processing of the images and what one should or, rather, shouldn't do in generating the final result. I'd also disagree with the idea that the goal is (always) a single background layer in Photoshop. That, again, goes into the editing of the image. But to that end, I'd suggest that creating a single background layer in PS is likely not the goal in a lot of cases. Rather I think a lot of people would create the combined image via layers and masks so that each layer can then be edited separately as may be needed to optimise the final result. Sorry, but I see large differences between the two.
As far as noise, look back earlier in this thread. Bart and I both brought up the idea of maximising SNR with HDR. Is noise an issue just for me? I'd hardly think so. Truth be told, I'm probably one of the more tolerant of image noise on this board. Unless one is going for a specific 'look' then maximising SNR is the goal of pretty much any photograph. It's the whole reason ETTR came into vogue. HDR - whether the 32 bit form or the (manual or automated) blended image form - is, for all intents and purposes, an extreme form of ETTR.