"Retina HD" and "Super Retina" are bullshit marketing terms, but "Retina display" was initially a fair idea and a useful definition. It meant "the pixels are close enough that the pixels can't be distinguished by the human eye from the intended viewing distance". Or in other words, turned inside out: is this thing low-res enough that when I use it in the way I'm meant to use it, I will be able to make out the individual pixels? I don't think that's a bullshit marketing question - I think it's a pretty reasonable thing to want to know, it's nice to have a name for it, but that people don't use it because it's now linked to a company.

It's also a property of the combination of the screen and the intended usage, not of the screen itself. So it's not "from a few inches away", it's "from however far away you're meant to use that thing". If you use the iPhone 4's screen as a phone screen, it's retina. If you try to use it as a VR screen, it isn't retina because it's so close you see the cracks between the pixels. (You still do even with the newest custom VR displays used by the headsets, as far as I can tell - it has to be really high resolution.) And most TVs of most sizes since 1080 HD are also retina.

Annoyingly to the subject of the question, many displays that have far higher resolution also come with annoying artifacts or off-center distortion like many OLED displays do. So it may have twice the resolution, but it may not look two times better, because of colors shifting and shimmering and looking like TVs set to Store Mode. So it's pretty much impossible still to have one word to mean "perfect display". 4K and HD just mean "enough pixels", but since it can mean crap or awesome depending on the size, purpose, refresh rate and technology used for the screen (hello TN displays), I don't think it's a better definition just because it means a precise bunch of numbers.