Just wanted to add one thing, not as a correction but just because I learned it recently and find it fascinating. PAL televisions (the color TV standard in Europe) actually do store one full horizontal scanline at a time, before any of it is drawn on the screen. This is due to a clever encoding used in this format where the TV actually needs to average two successive scan lines (phase-shifted compared to each other) to draw them. Supposedly this cancels out some forms of distortion. It is quite fascinating this was even possible with analogue technology. The line is stored in a delay line for 64 microseconds.
See e.g.: https://www.youtube.com/watch?v=bsk4WWtRx6M
At some point, most NTSC TVs had delay lines, too. A comb filter was commonly used for separating the chroma from the luma, taking advantage of the chroma phase being flipped each line. Sophisticated comb filters would have multiple delay lines and logic to adaptively decide which to use. Some even delayed a whole field or frame, so you could say that in this case one or more frames were stored in the TV.
If a motion adaptive 3d comb filter (which requires comparing successive frames) was present on a TV, you can bet that it would be plastered all over the marketing material for the TV.
You can decode a PAL signal without any memory, the memory is only needed to correct for phase errors. In SECAM though, it's a hard requirement because the two color components, Db and Dr, are transmitted on alternating lines, and you need both on each line.
Just wanted to add one thing, not as a correction but just because I learned it recently and find it fascinating. PAL televisions (the color TV standard in Europe) actually do store one full horizontal scanline at a time, before any of it is drawn on the screen. This is due to a clever encoding used in this format where the TV actually needs to average two successive scan lines (phase-shifted compared to each other) to draw them. Supposedly this cancels out some forms of distortion. It is quite fascinating this was even possible with analogue technology. The line is stored in a delay line for 64 microseconds. See e.g.: https://www.youtube.com/watch?v=bsk4WWtRx6M