With regard to your heading: Scan lines involving CRTs refers to electron beam(s) sweeping back and forth, creating a blank raster on a phosphor screen. With no signal, you can see these scan lines near the screen.
A video signal creates an image by modulating these scan lines. Vertical resolution differs from scan lines. This resolution is the number of alternating black and white test pattern lines visible from the top to bottom of a screen. When TV images are scanned at the source, a scan line can miss a detail entirely or two scan lines may straddle details. With vertical motion, this occurs more often. As a result, vertical resolution with most TV is typically only about 0.7 the number of scan lines for stationary images and about 0.5 the number of scan lines for moving images.
Horizontal resolution is how much detail is visible along each scan line. Usually this is the number of alternating black and white lines visible along a scan line length equal to the height of the picture. To obtain the full-width horizontal resolution for 4:3 screens , multiply by 4/3 = 1.33. For 16:9 screens, multiply by 16/9 = 1.78. For CRT displays this resolution depends on how finely the electron beam spot(s) can be focused, how much contrast can be obtained, whether the CRT has a fine-pitch shadow-mask screen (if direct-view), and whether the video circuits can pass the higher frequencies carrying fine details (good bandwidth). Other factors such as the optical resolution of lenses and the optical pitch of elements in rear-projection screens are involved with projection TVs. -- John