Aspect ratio refers to the relationship between the width and height of either an image, or a pixel. The latter is simply referred to as the pixel aspect ratio.
Common video aspect ratios are 4 by 3 and 16 by 9. Often these are referred to by the decimal result of dividing the width by the height. So 4:3 becomes 4 divided by 3 which equals roughly 1.33. 16:9 is thus often referred to as 1.78. Cinemascope, a common widescreen format is called 2.35.
Pixel aspect ratio refers to the effective pixel width to height ratio after an image has been stretched to its final viewing aspect ratio. While pixels are always stored as perfect squares in computer memory, for final viewing, they may be stretched to a different size.
For example, an anamorphic image stretched to twice its actual pixel width for display has a pixel aspect ratio of 2:1, since its source pixels will be displayed twice as wide as they are tall.
Traditional standard definition video formats have unusual pixel aspect ratios. Both NTSC and PAL video formats display at a 4:3 aspect ratio, but have source pixel resolutions of 720 x 486 and 720 x 576 respectively. Thus their pixel aspect ratios are not perfect squares but display with an aspect ratio of 0.9 for NTSC and 1.09 for PAL.