As simply I understand it, frame rate is the number of still images that can be displayed on the screen and refresh rate is the number of times the monitor can draw image on the screen.
So, consider a hypothetical computer delta made solely for video playing. If the refresh rate of the monitor is 25Hz and the frame rate of the video is 25fps, then would the video play smoothly?
The flicker fusion threshold, that is, the frequency with which sequential images can be displayed without flicker, varies from person to person, and with the brightness of the image, amount of detail changed between frames, etc.
That said, 25 fps is slow. NYC subway lighting supply was 25 Hz ("cycles per second") and produced noticeable flicker, even though incandescent lamps have thermal inertia and smoothed out the variation (actually, there were 50 light peaks per second, but even that flickered!). "Most people do not detect flicker above 400 Hz."
LCD displays are more forgiving, because the backlight is always on and pixels change slowly compared to the refresh frequency, but LED and OLED displays would exacerbate the issue.
BTW, birds see faster. The flicker fusion frequency for some birds is >120 Hz. A pigeon won't enjoy movies, but African grey parrots apparently enjoy TV on LCD.
