Im not sure what you are trying to understand...there is dpi and there is resolution. Most HD TV's and mainstream monitors run at 1920x1080 resolution or pixels. They will have different dpi based upon their physical size.
Some larger and very expensive monitors and a couple of very expensive tv/monitors have higher resolution (2560x1600, 4000x2000, etc) but they are the exception.
You can have a small device with fewer pixels and most of them do not display 1920x1080 - they drop every other row or column and your brain averages out the picture. They do store the information in the 1920x1080 format.
Part of the issue is how far away are you from the picture...the small device is what - 6" away while the big 65" tv is 6 feet away. Distance matters in your perceived resolution.
Not sure if that helps or makes it worse...