Resolution is how many pixels a display has in length x width format (the more, the better when choosing a PC monitor).
The difference between high definition and standard definition images is the number of pixels contained in the image on display. 

SD or Standard Definition came before HD or High Definition video 

SD displays have the smaller resolution of 720 x 480 interlaced screen size 4:3 ratio and
480 lines of vertical 
resolution (720 x 576 PAL).

Standard definition has always been a 4:3 aspect ratio with a pixel resolution of 640 × 480 pixels.
In PAL regions such as Europe and Australia, the vertical 
resolution is 576 pixels, and the frame-rate has been reduced to 25 fps.

What is SD display?
Standard-definition television (SDTV or SD) is a television system which uses a resolution that is not considered to be either high or enhanced definition.
SDTV and high-definition television (HDTV) are the two categories of display formats for digital television (DTV) transmissions..

HD displays have a resolution of 1280 x 720 pixels, also known as 720p.

HD displays can also have a resolution of 1920 x 1080, commonly referred to as 1080p.

HD images have more pixels per square inch than standard definition videos therefore HD images can show much finer detail than SD images.

HD video refers to 1080p resolution, sometimes called "Full HD", and a noteable step up from 480p, generally referred to as standard definition (SD), or "DVD quality."
Is full HD 1920x1080?
1080p (1920×1080 px; also known as Full HD or FHD and BT.709) is a set of HDTV high-definition video modes, 1,920 pixels displayed across the screen horizontally and 1,080 pixels down the screen vertically; the p stands for progressive scan, i.e. non-interlaced.
Is 720p better than 1080p?
720p has an image resolution of 1280 pixels by 720 lines. 720p was the first available HDTV resolution. ...
By comparison, a 720p TV has twice the resolution of an analog TV picture.
1080i has a resolution of 1920 pixels by 1080 horizontal lines, INTERLACED.
1080p has a resolution of 1920 pixels by 1080 horizontal lines, PROGRESSIVE.
Which is better 1080i or 1080p?
1080i has a resolution of 1920 pixels by 1080 horizontal lines. ... 1080i was once the standard in HDTVs but no more. Its quality is not much better than the 720p TVs.

1080p has a resolution of 1920 by 1080 pixels, and it is a progressive scan, not interlaced, so it provides a picture with a full 2.07 million pixels.
Is 1280x720 better than 1080p?
A screen resolution of 1920x1080 (two million pixels when multiplied) should appear twice as sharp as a resolution of 1280x720 (fewer than one million pixels).
The p in 1080p and 720p stands for progressive scanning, which updates full frame images more quickly than traditionally interlaced content.

 4K video resolution is high-definition (HD) video that has four times the resolution of 1080p HD video. ...
 The Digital Cinema Initiatives standard for 4K resolution in the film and video production industry is 4096x2160 pixels.
The big difference has major advantages for 4K compared to the quality of a 1080P video.