The parameters are no different for real time rendering, but the actual thresholds for what is considered HDR are non enforced.
SDR / Standard Dynamic Range content (or "LDR" Low Dynamic Range content) were typically made to be displayed at around 100nits, if you are at a theatre, this will be the brightest something could be.
As soon as you start producing content that goes above that, you are creating content with a larger dynamic range and you need the display to be able to view it.
HDR movies are available that range anywhere from 500 nits to 4000 nits, with a view that in future this will go as high as 10,000.
TV manufacturers were desperate to launch new TVs and a new format and in doing so they started producing displays that went above the SDR technology, but there was huge variation in capability. Displays were being sold as HDR that were not really much higher than an SDR display.
Consumers got confused, content didn't look much better if better at all and confidence was low. The manufacturers had started selling a new technology that was not standardized, which would have made it difficult to sell an improved set later on down the line.
A few of the manufacturers go together in an attempt to set a threshold and standardise HDR capabilities.
UHD Premium was created. In order to be a Ultra HD Premium display you needed to be able to display 1000nits of brightness and less than 0.05nits on screen simultaneously.
Now because the manufacturers were also trying to sell OLED screens, which were not able to come close to this threshold, they bent the rules and lowered the requirement for peak OLED screens to 540nits, because they could go darker 0.0005nits with ease. This was deceptive, as HDR content is all about the extra brightness and not about dark imagery.
Sony famously refused to participate in the standard as they were concerned that this would not leave enough low/mid range products capable of meeting this criteria, which was where they typically sell the vast majority of their displays.
So they went with their own format
This meant that the TV could accept and 4K and HDR signal, but was no guarentee of anything else.
More recently they have backpeddle and started referring to their TVs as XDR / EDR (Extended Dynamic Range).
Because as the others had previously, they became aware that they were going to sell a load of TVs as "HDR" and then consumers would not understand that the experience would be better with new models later on down the line and would not feel compelled to purchase an actual HDR TV form Sony.
So there has been loads of politics and bullshit from Day Zero of HDR and Displays.
That probably hasn't fully answered your question, but it's hard to keep it briefer than that :P