Most 8-bit panels (16.7 million colors) are actually 6-bit panels (262k colors). Modern panels make up the extra 2 bits using something called FRC. Basically, they rapidly flicker between the two colors they can show, to simulate the in-between color that they can't show. So if the panel is supposed to show Red 243, but because it's 6-bit it can only show R240 and R244, it will flicker between R240 and R244, showing R240 25% of the time, R244 75% of the time. Over time, that averages out to R243, and that's what your eye sees.
https://en.wikipedia.org/wiki/Frame_rate_control
LED and LCD monitors actually both use LCDs, but the LED monitors use a LED backlight. The LCD monitors use a CCFL (fluorescent lamp) backlight. That has some small implications for color, but isn't really relevant to the noise you're seeing. The important thing is that everyone switched to LEDs about 7 years ago. So LED monitors are newer than LCD monitors.
The newer LED monitors use newer panels whose pixels can change shades more quickly. So their FRC happens at a higher frequency where it's invisible to your eye (well, most people's eyes - a few of us are cursed with vision which lets us see fluorescent lights, LED car tail lights, even monitor backlights flicker at up to several hundred Hz).
Older LCD monitors use older, slower panels so their FRC happens at a lower frequency, and the pixels can look like they're noisy or (if your eye is moving) swimming/swirling. Or sometimes the panels were so slow they couldn't do FRC without it becoming terribly obvious, so they used spatial dithering instead. That's where nearby pixel colors are tweaked slightly so the average of (say) 4 pixels is the average of the 8-bit 4-pixel quad even though each individual pixel is displaying a 6-bit color. This sorta works in most real-world images, but becomes really obvious (noisy) in images with solid blocks of color or smooth gradients.
http://www.tftcentral.co.uk/featurescontent.htm#dithering