ffmpeg- What's the difference between "NN000/1000 fps" and "NN000/1001 fps"?
Yes, 24000/1000 is 24 fps and 24000/1001 is 23.976fps. Some refer to the X/1001 frame rates as "drop down" (as in "dropped down from the integer") but this is easy to confuse with "pull down" which often refers to the cadence of frames when fitting 24 or 25 fps material into a 30 fps program.

You can also think of these notations as 24,000 divided by 1,000 equals 24 and 24,000 divided by 1,001 equals 23.976023976 repeating. This notation is also the exact same thing as saying 24 divided by 1 equals 24 and 24 divided by 1.001 equals 23.976023976 repeating. It is, of course, quite ridiculous to articulate the repeating decimal values.

The 1001 options and their resulting notation are a legacy from analog color television systems. As Mulvya points out "it's because that's the smallest set of numbers that represent the value as integers". These standards are still around today mainly for backwards compatibility (with black and white television sets) and 'cause that's just the way TV grew up. Prior to color television, the NTSC frame rate was actually exactly thirty frames per second.

As for the 30000/1000 and 30000/1001 notation it comes from the NTSC video standard. "30"fps NTSC is actually displaying 30/1.001 frames per second (sometimes referred to as "29.97" or "30DF" for short, but to be precise 29.97002997... repeating frames per second). Due to this slight difference (.01%), NTSC uses either Drop-Frame (DF) or Non Drop-Frame (NDF) time-code counting. Drop-Frame "drops" frame counts in a pattern such that every ten minutes the time-code duration will correspond to the actual playback duration. No image frames are dropped and this was mainly a consideration for broadcasters fitting their programs with commercial breaks. Non Drop-Frame on the other hand more accurately represents a count of the total number of frames in a program (for those who enjoy counting in base 24:60:60:30...)

As for 25000/1000 there's no 25/1.001fps standard because 25fps is a PAL standard and PAL video systems were engineered using 50Hz AC power which did not have the same issues as NTSC when color came about.