HDRI vs HDR for TV
The short answer is that the terms are substantively different in meaning, both technically and subjectively. However, HDR for TV is certainly not just a marketing term, and I can't think of a more appropriate term for what HDR capable TVs are offering.
I began working with high dynamic range imagery for feature film production at Digital Domain based on the work of Greg Ward Larson, and Paul Debevec back in 1999. I think I was the first to develop a process for lighting CG with HDR images in real time using preprocessed spherical convolutions of HDR environment maps (boy that's a mouth full). If I recall correctly Paul did a paper on HDR for real time in 2001, so there were probably a number of people who were doing similar things around that time. In the same year, 2001, I did a panel on the future of color at SIGGRAPH with Roger Deakins originally, but Allen Daviau filled in last minute when Deakins was pulled onto "A Beautiful Mind". Also on the panel was Neil Robinson (then from ILM), and Beverly Wood from Deluxe Laboratories. So I've been involved with HDR as originally defined from pretty close to the beginning, and I've had the opportunity to learn from some amazingly talented people.
As it relates to the usage of HDR for TVs and modern consumer distribution channels I've recently had the opportunity to work with Jenz Merrill who is in charge of the HDR pipeline for Amazon Instant Video which is the first commercial HDR delivery, and I'm also good friends with Thad Beier who is the Director of Imaging Platform Workflow at Dolby Labs.
Although I'm not directly involved in the work at Amazon or Dolby Labs, and just to be clear they are different workflows, I've seen what's being done and I can say the results are spectacular.
One Example from "Mozart in the Jungle"
I've recently seen some of the work Amazon has done over at Technicolor, and it is beautiful. In the color suite Technicolor had an HDR monitor next to a standard HD monitor, both calibrated perfectly, and both looked beautiful. One shot in particular from "Mozart in the Jungle" stands out. The shot is inside a library and on the perfectly calibrated studio grade HD monitor it's beautiful, warm colors, great composition, all in all a fantastic shot. However on the HDR monitor it's breathtaking.
Typically a very good HD tv can output up to 400 nits of brightness (one nit is equivalent to one candela or candlepower per square meter). I'm viewing this web page on a MacBook Pro Retina display at full brightness and reviews say that it's about 300 nits. I'm told the HDR monitor that I saw at Technicolor was 1100 nits! Not mere percentages brighter but nearly 4 times brighter then my MacBook pro, and nearly 3 times brighter then a top of the line HD tv.
Even more dramatic is the fact that this additional brightness does not come at the cost of increasing the brightness of the dark areas of the image. This is correctly referred to as dynamic rage not simply brightness or contrast.
It is hard to truly internalize the differences between the displays without seeing them side by side, because it isn't simply a matter of showing more exposure latitude in the image. You can do that on any display at any brightness by compressing the dynamic range into the displayable range. An HDR monitor is displaying dark element of the frame like books on a bookshelf in shadow at a very similar overall light output as an HD monitor, and a bright element like a white wall also at a very similar overall light output as the HD monitor. What's different is that the HDR monitor can keep going in both directions.
HDR in TV
Back to the shot from "Mozart in the Jungle". Between the monitors the dark books look about the same and the light walls look about the same, but the stained glass window in the background is completely different. On the HD monitor the window blooms into bright overexposure looking exactly like what you'd expect by shooting in a dark room with a bright window. The HDR monitor however hits that brightness and more, showing the beautiful colors of the stand glass window not by crushing the brightness into a displayable range but by literally outputting more light. At up to 1100 nits the colors of that stand glass window are explosive.
As I was sitting in that room with the various displays showing the same shot, the stained glass window on the HDR monitor was by far the brightest thing in the room, and the colors unbelievable. On top of this, the darkest elements in that image in the shadows of the bookshelves are some of the darkest things in the room yet the colors and details are still visible. It is an amazing thing to see.
HDR for TV is not a technical improvement that looks like crap like high frame rate and motion smoothing, or a numbers game that's more or less superfluous for TV size images like 4k vs 2k. HDR as actually higher light output, is a real improvement both creatively and technically.
HDR in Imaging (HDRI)
So what's the difference? The difference is that the way we used HDR for capture and manipulation of images was originally mostly intended to mean recording absolute light values outside of any concept of displayability. It is the secondary effects of that capture that are visible. For example the ability to use an image as a light source in a cg rendering because the light sources captured in the HDR image are recorded with their actual values and in proper proportion to the reflected light in the image like walls and floor.
Typically the difference between the light output of a light source and that of a reflection surface like a white wall is many orders of magnitude. Even a 1100 nit HDR TV is incapable of representing these ranges literally in most cases, and it's doubtful that you'd want it to. What's being shown is the additional latitude that has been part of the image all along, including and especially film, but not displayable in the final result without having negative affects on the 'look' of the image such as reducing the contrast. This gives us post processing latitude for moving exposure up and down and adjusting color without too many artifacts in bright or dark areas.
As is the case with the shot from "Mozart in the Jungle" HDR tvs and the new standards such as REC 2020 for tv and P3 for digital cinema are delivering more of what was already captured in the extended latitude (shoulder and heal) of the film or sensor used. Unlike HDRI, none of this requires a significantly different capture process. Although, DPs and directors will definitely want to start taking it into account. Kind of in a similar way that HD had an impact on the makeup department.
How to evaluate an HDR TV
Scenes with low contrast such as characters talking in a normally lit interior shot should appear almost identical even in a side by side comparison (give or take overall brightness). Shots like this may demonstrate improved color on an HDR tv but the differences will typically be too subtle to notice. Scenes with visible light sources or dramatic use of color; day exteriors with sky, nighttime club scenes with neon and stage lighting, just about anything by David Fincher, all will look dramatically different on HDR TVs, but not because the contrast has been cranked up, the contrast should seem roughly the same as a good HD tv, the darks and lights just go further.
Existing (REC 709) content should look generally the same between HD and HDR tvs. If they don't something is wrong with the setup of one or both of them. Post color must be redone to include the additional range, and only that shows off the real power of HDR tvs.