What is the Image P3 color space in Photoshop meant for?

My article discusses the gamut in general, but doesn’t help much in differentiating the variations of P3 except for this one sentence:

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The DCI-P3 color gamut started out as a standard for digital cinema because it’s based on the color range reproduced by the type of digital projector you’d find at a movie theater. Apple created their own version called Display P3, adapting it for computer displays and making some aspects of it more consistent with sRGB.

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But that’s not detailed enough. D Fosse and thedigitaldog have filled in more specific details about the difference, like the white point shift.

This is one way to summarize the differences:

• DCI-P3: This industry standard is specifically intended for cinema display, because of its white point optimized for cinema projectors, and because its luminance is so low. According to Wikipedia and color.org, DCI-P3 uses a white luminance of 48 cd/m²… which is absurdly dark for computer use. But it’s perfectly reasonable for projection in a dark room like a movie theater, which is what it’s for. 
• Display P3: This Apple derivative uses the DCI-P3 gamut, but to be appropriate for use on common computer and mobile displays, this standard does not limit the luminance to 48 cd/m². According to the display presets for the Apple Pro Display XDR and the Liquid Retina XDR screens which both use P3, luminance is limited to 160 cd/m², which is appropriate for SDR consumer/mobile/web viewing (the largest market by far), but too bright for print or SDR cinema (OK for SDR TV viewing). 
• Image P3: I’m less sure as to what this Adobe variation is about. The Image P3 profile is installed inside a folder that’s accessible only to Adobe applications, so Image P3 might be an Adobe-only thing. If you compare Image P3 to Display P3 in Apple ColorSync Utility, Image P3 uses the same RGB primaries, but a different white point, and a different rendering intent (see below). At this point someone else (ideally from Adobe) is going to have to explain why they chose those differences because I don’t know. 

What we do know is that while all three standards use the P3 color gamut, the reason they’re different is because of variations in other specs like white point, luminance, TRC/gamma, and rendering intent.