Analog color TV (NTSC, PAL & SECAM) is made up of four signals - a black & white signal (luma) and two color difference signals (chroma) and framing/synchronization signals. One field of NTSC is 262.5 lines of 63.555555uS and two fields make up one interlaced frame. However, the Atari 2600/7800 doesn't bother with interlacing so each frame is only 262 lines. Officially, only 241.5 lines are active picture (21 vertical blank) and only 52.855555uS (or a little over 83%) of those lines are active video (10.7uS horizontal blank). So an interlaced frame could have up 483 active lines although a bunch of those will be lost on most TVs to overscan.
Okay, what about horizontal resolution? The TV industry often uses the term "TV lines" to describe the horizontal resolution of a CRT, which is a very confusing metric and is typically 75% of the value we normally consider to be horizontal resolution - the number of active resolvable pixels per line. It's also almost entirely meaningless because it ignores the limitations of the input signal, which brings us back to chroma and luma and how they get to the TV.
If each of the three signals is sent separately (ignoring the sync since it happens outside of the active picture) then it's a component connection. This also means that each of the three signals have virtually unlimitted bandwidth and horizontal resolution. An NTSC DVD uses 13.5MHz sampling (6.75MHz bandwidth) producing 858 samples per line of which 720 are encoded (which includes some horizontal blank). (Actually, the chroma bandwidth is 3.375MHz, half of the luma bandwidth, due to downsampling before encoding.) Component is also the only time when the resolution of modern displays could be exceeded by the source material.
Next is S-Video which combines the two chroma signals into one using a 3.579546MHz carrier, which therefore limits the chroma signal to 3.579546MHz or 455 samples per line (378 active). The luma signal is not limitted, but is typically less than 7.159091MHz, or 2x the chroma carrier, for 910 samples per line (756 active).
The next step is to combine everything into a single composite signal (which can then be modulated to a given RF frequency for broadcast). This is also where color aliasing comes into play. Ideally the chroma bandwidth is limitted to less than 1.3MHz (137 active per line out of 165 samples) and luma bandwidth to less than 2.27MHz (240 active per line out of 288 samples) to prevent overlap (luma bandwidth + chroma bandwidth < chroma carrier). Okay, what happens if they do overlap? That's when aliasing occurs - instead of detail you get colors. Unfortunately, the 7800 320H modes output pixels at 7.159091, which is twice the chroma carrier and so any on/off patterns will generate color instead of detail.Â