Of course, what makes things confusing for consumers, is that each format applies HDR in slightly different ways. HDR10 is considered more generic as its parameters are applied equally throughout a specific piece of content, and the TV decides how to display the information, while Dolby Vision is considered more precise in that it can adjust HDR parameters on a frame-by-frame basis, based on the capabilities of the TV.
This state of affairs means that some HDR-enabled TVs or video projectors are compatible with content using the HDR10 format, and to make things even more confusing, as of 2016, the Ultra HD Blu-ray Disc format has only implemented HDR10, although there is no technical limitation that wouldn't enable Dolby Vision to also be used.
On the other hand, the way Dolby has structured Dolby Vision, licensed and-equipped TVs supporting that format also have the ability to decode both Dolby Vision and HDR10 signals (if this capability is turned on buy the specific TV maker involved), but a TV that is only compliant with HDR10 is not capable of decoding Dolby Vision signals.
In other words, a Dolby Vision TV also has the ability to decode HDR10, but an HDR10-only TV cannot decode Dolby Vision - in this case, the TV will just ignore the Dolby Vision encoding and display the image as an SDR (Standard Dynamic Range) image.