I would take a wild guess and say that your textures might be huge, and your objects are are unnecessary too high detail. You can see that the rendering itself is still around 8 seconds (even though the realtime and output resolutions are not the same - but they are close, so it is not big impact on the speed)
If you check your second video, you can see that it takes the most time on GPU Geometry Setup, and Load GPU materials steps... The saving of the files is pretty fast, so I don't think it is due to your slow HDD or network drive (which is visible you are not using).
Also, the option of saving frames and video at the same time shouldn't affect the time per frame, as the video is composed out of frames in the end of the rendering.
And, it can't be any of the Image styles options (like denoise, blur, bloom) as you can see in the same video that applying image styles takes about 1 second or so.
You always need to account for a bit more time per frame when comparing just one image to an animation, but that said, your case does look a bit longer than it should, so like I said, I'd look into checking geometry if it can be optimized, and check all the textures you might be using in your materials. For instance, just apply gray material to all objects and see if the Load GPU materials step is any faster... that will eliminate the textures theory.
Cheers