It's complicated. If taking a still image, shutter speed control would give you all the clarity you want. But the perception of moving images is also affected by frame rate, the number of key frames or I-frames and P-frames, the refresh rate of the screen you are viewing them on and the conditioning of the human brain. And with a stationary camera, as most CCTV cams are, the speed that the subject moves across the frame is a major complication.
Whatever frame rate and however many key frames you set for your video, your monitor will probably show you 60 images per second since most monitors have a 60Hz refresh rate (or 50 images per second if the refresh rate is 50Hz). If the video doesn't contain 60 (or 50) frames per second then the monitor will duplicate frames to make up the total. This creates flicker and a degree of blur depending on the maths involved. So the optimal video diet for a clean viewing experience is 60fps (or 50fps).
Next you have to compute the optimal frame rate for the subject matter. If it is a stationary subject, 1fps is plenty to capture clean images. If it is moving only slowly, maybe 5-10fps would deliver clean images. But if the subject is moving quickly (which in the movie industry means it crosses the frame in less than 7 seconds) then you will need to boost the frame rate to capture it clearly. That's because there are so many pixels changing from frame to frame. If you don't capture in the optimal 60fps (or faster) then your software will compensate for the missing data by interpolating new frames in between the existing frames resulting in a smeary or motion blur effect - which is often wanted by movie makers but is unhelpful for CCTV. Traditionally, 24fps has been the optimal rate for shooting movies because motion blur helps to deliver realism, ie that's what the naked eye sees. But it's the last thing you want in CCTV footage. It's apparently the last thing that video game players want too since their on-screen action comes fast and furious. So most games players demand 60fps for clarity and no motion blur to jolt them out of their virtual world.
Some recent animation movies were shot in 48fps and higher for the crisp, clean imagery it made possible.
The final piece of the jigsaw is video compression. Whatever codec is used to compress video - typically H264 or H265 - it does its job by selectively losing data. It splits video up into frames which are very similar to the preceding frame and frames which contain a lot of pixel changes and it produces video which is made up of a number of accurate or pure frames, called I-frames plus a greater number of predicted or interpolated frames, called P-frames. When the video subject is moving quickly, the amount of interpolation is greater and the quality of the P-frames is lower. It's the only way the video can be forced to fit onto a memory card or to play smoothly over a network. But by increasing the frame rate to 60fps, the number of I-frames can be increased and the number of interpolated frames reduced, resulting in a cleaner, clearer video with much sharper individual frames.
You can test this out for yourself by playing some 30fps and 60fps videos on Youtube and pausing them to compare the clarity of the individual frames - assuming you have a computer which is powerful enough to play 60fps. Look for 1080p videos to compare as 4k videos won't play at 60fps on most PCs.
Here's something to read:
5 reasons for 60 fps - Paul Bakaus' blog
What a good test result to see ipOsX! I would like to understand the technicalities better. Would you please take the time to help me understand why, if the shutter speed etc is exactly the same at 24fps as at 60fps, the clarity is different. Would the clarity be identical in each case if you viewed a single frame instead of pausing the video?