A plain ND-filter only have one effect ... It prevent less light to reach the sensor, it's like sunglasses for your lens.
The reason you want to get in less light, usually is due to that you want to modify the shutter speed ... & specifically make it slower.
You can make the shutter slower in other ways also ... you can stop down the aperture if it's not fixed. You can adjust the ISO to a lower value making the sensor less sensitive.
But if you have a fixed aperture ... already use the lowest possible ISO ... & using the camera during bright daylight ... then the shutter will be around 1/1000sec. So if you want to to get a slower shutter the ND-filter is the only thing you then can use.
Why you want a slower shutter have nothing to do with if you're videoing or taking stills ... it's only depending on what you want to achieve.
With a slower shutter moving objects in the motif will move slightly during the exposure ... meaning they will have motion blur. How dark the ND is will regulate how slow the shutter will be & by that how much motion blur the object will have.
In video you want motion blur to get rid of that "sticky" look you get when all frames are pin sharp ... & also get away from the stuttering that easily occur when to little motion blur is introduced ... search for "the 180 degree rule"
Here 3 levels of blur introduced in the video ...
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When you're taking stills this is the effect you are after for instance...
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Or like here... getting smooth water.
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