The Pixel's HDR+ mode is a much improved version over the older variation that has been available on past Nexus devices, and although it is technically still HDR+, Google has added plenty of adjustments to it that makes it even better and is part of why the Pixel and Pixel XL were so highly rated in the camera department. HDR+ on the Pixel phones was also designed to be left on all of the time as it just takes a really good photo, and this alleviates some of the hassle that the more average consumer may have been feeling when trying to decide when to use HDR+ on older devices.
Comparing the two, HDR+ on Nexus devices that have it and HDR+ on the Pixel and the Pixel XL are not too different from each other. They both take a number of still photos when the camera app's shutter button is pressed and then it takes the best shot of all the photos that were taken and it uses this as the main image. The rest of the shots that were taken aren't tossed out, but rather used to layer the image for a higher quality photo. The difference in the versions of HDR+ lies in the speed. HDR+ on the Pixel is much faster and immediately begins storing frames for the photo as soon as the app is opened. This allows the camera to produce a photo much quicker as it already has a number of frames ready to go, and is just waiting on the user to point the viewfinder and press the shutter button to start finalizing the process.
That being said, there are two different variations of HDR+ that can be found on the Pixel and Pixel XL, which are HDR + Auto and HDR+ On. Both work in much the same way and will result in a similar photo at the end but HDR+ On will end up putting out a slightly better photo that has a little bit more balance to it. Pictures shot from this mode can also end up looking brighter so it's the optimal mode for people that want their pictures to come out with more light in them, as they won't have to tune the image with brightness as much after the fact, if at all. The quality of images and how many burst shots are taken with the Pixel's HDR+ modes can also depend on how much available light there is in the image you're trying to take, and if there's less light for example, than the camera might try to provide more bust shots before moving onto the next step and finalizing the image. The downside perhaps is that HDR+ On will take just a little bit more time to finish capturing the image than HDR+ Auto, which is a big reason why many users may decide to stick with HDR+ Auto for their chosen mode. In either case, both modes are improved over what Google was using before, will likely only continue to get better as Google updates the camera to fine tune the experience.