"P" means progressive, ie full "frames" and not "interlaced". Standard Definition (SD) can be progressive or interlaced depending on the source and/or viewing device. Typically, SD material is (in the USA) considered to be about 480 vertical lines of resolution maximum (although NTSC does officially support more), where as HD is at least 720.
I think the D800 has the option of recording at SD or HD formats, but I do not know what the HDMI direct output is, but I would guess that it matches whatever setting that you have it to record to. Both your resolution, frame rate and i/p settings will probably output at whatever you set them to record at. But this is just a guess. Even my D3 can send a video feed out at either 720p or 1080i and I am pretty sure that 1080i is 60 fields per second and 720p is 30 frames per second for the D3. The D800 also may be able to output directly at 24 frames per second. If so, this will be of significant interest to filmmakers and I would guess that it does allow this ability.