HDR10 is the free licensing standard of HDR (AKA it costs companies no money to implement it.) Dolby Vision is a fee based standard (companies like Apple, Samsung, Denon, etc pay Dolby for the rights to implement their standard). Dolby Vision is built upon HDR10.
Basically it's a battle between HDR10 and Dolby Vision. Like any format war (Bluray vs HD-DVD), it's confusing to the end consumer.
There's no real known differences/benefits to Dolby Vision other than their cool little logo at this time.
What does that mean for the iPhone? Both iPhones (X and 8 Plus) support HDR10 and Dolby Vision. The X will do a better job at supporting HDR content because it uses an OLED display, which means each pixel can have it's brightness controlled. HDR only matters though if you're watching HDR content. Pretty much the only HDR content at this time will be the movies you'll find for sale in the iTunes store. Regular content such as apps, the home screen, and regular videos won't be able to leverage HDR10 and Dolby Vision.
Basically, I wouldn't worry about HDR right now on the iPhone. It's going to take a few generations before we really start to see the benefit of it on a large scale.