DVD's are SD and limited to 480 (NTSC) and 576 (PAL) - HDMI "upres" players convert the 480/576 signals up to 1080, but they are still playing MPEG2 files on a disc that are 720x480 or 720x576
HD is anything over 720P, but tends to be descriptive of 1280x720, 1440x1080, and 1920x1080 - the official standards of "HDTV", but 2K and 4K are high resolution and even "high definition" but there are no TV's on the market that can play those formats..... yet.