In plain language
Digital Cinema Initiatives defines the formats used in commercial projection. DCI 4K is 4096 x 2160; consumer UHD is 3840 x 2160. Same height, 256 pixels difference in width, slightly different aspect ratio.
The name also attaches to DCI-P3, the cinema colour space, which is a separate thing entirely.
Why it matters in your setup
Mainly with projectors and computers. A projector may accept a DCI timing where a television will not, and a graphics card can be persuaded to output one. If a source offers a 4096-wide mode and the display refuses it, that is the distinction biting.
For ordinary playback it rarely comes up: streaming and disc content is UHD.
What the DR HDMI 8K does with it
DCI formats with DSC are among the supported signals listed for the DR HDMI 8K. If a DCI mode is not being offered, its EDID readouts show what the display is actually advertising, which settles whether the mode is unsupported or simply never announced.
Need the hardware?
Open the DR HDMI 8K product page on HDfury.uk.