Just throwing my two cents in, all of what tepples said is correct to my knowledge, but CRT's with a comb filter are also technically "tuned" to display 480i. Not all CRT's are even created equal in this regard unfortunately.
I have a monitor that lets me select which filter I want to use (and also offers a "both" option). Simple knowledge of how the comb filter works suffices (and lidnariq already mentioned it), but I'm just going to share my favorite example (with some photos, from my AV-modded famicom).
An easy way to test on this monitor is just to start a game of Dragon Warrior/Dragon Quest. The bricks in the King's chamber have two lines of red, followed by one line of gray, followed by two more red. On TV's with a comb filter, you won't see the gray lines of the bricks properly, and the topmost red line is also impacted by the black one above it. Only the middle red line looks largely correct in the comb filter.
Of course, comb implementation may vary depending on the hardware in use and/or the software in use if applicable.
Anyway, here are some pictures. It's hard to see here, but the comb filter does do a nicer job of keeping the edges of colorless things crisp; this is the most noticeable in text boxes with black-to-white transitions. So in a sense a CRT with a comb filter is likely sacrificing some vertical clarity for better horizontal clarity if used for progressive signals.
Click on the images for the full resolutions (warning: around 9-10 MiB each).
Notch filter only:
Comb filter only:
Additionally, I have seen some LCD's and plasmas that do a relatively good job (not perfect - they often still will interpret 240p as 480i and apply comb filtering - but good in that they don't do any additional processing beyond scaling and have a good analogue -> digital conversion and scaler inside).
My parents have a 50" Panasonic plasma from around 2008 which does shockingly well; I played the entire Legend of Zelda on it over a weekend when I was visiting and never noticed any major issues. It only messes up badly with 60hz flashes, where you'll clearly see the interlacing pattern, and of course it has the comb filter cross-talk. With S-video systems it looks absolutely great in most circumstances. I also played some original Playstation games via S-Video (using a later PSX with the better video encoder) and it looked just about flawless, even with my eyes under a foot from the panel, due to the lack of a comb filter in S-Video and the already rather good handling of analogue signals that the set posesses. My earliest playstation (SCPH-1001, November 1995) was a bit blurrier in S-Video but also looked quite good. It's just a shame that the '2C02 doesn't expose a separate chroma signal (which has been said probably over 9,000 times now), but when the image isn't scrolling NES/FC games still look very sharp for the signal type they're using.
But some other TV's I've seen like to try to blur the edges of objects when the screen scrolls or a sprite moves. The result looks almost like hq4x or something, but it only happens to things that are moving on the screen.This was with a friend's OLED when I showed him Kirby's Adventure (on my Wii through virtual console, via my Wii with component cables, even). This happened in both 480p and 240p modes (Wii VC NES games usually run in 240p unless the Wii is configured to use 480p in system setttings). I don't think this friend is dumb enough to leave motion interpolation on (he owns a colorimeter and calibrates to D65, so he at least cares about picture quality), but basically we have no idea what kind of "cleaning up" modern TV's are doing and it can vary wildly between sets.
I also noticed substantial noise I never see in component video on any of my sets, leading me to suspect little attention was paid to the quality of the analogue video inputs and they were just thrown on as an afterthought (which they likely were).