Yup, there’s 3 main areas where everything can change:
1. Physical hardware
In camera, the physical size of the sensor and how it is used makes a difference, as does the quality of the sensor, and the quality of the lens. For instance my 5D IV uses the whole full frame sensor when shooting 1080p and resamples the resolution down to 1080p. When shooting 4K, it uses a cropped area of the sensor instead with no sampling. This effects the amount of light that is absorbed as well.
2. Pre-shoot settings
ISO, shutter speed, aperture, the focus point/mode of the lens, AF tracking, stabilization and other settings will all affect how the camera shoots an image/video. Is it in focus? Can the sensor handle the ISO / low light?
3. Video file settings
How the camera saves the file makes a difference. The bitrate, compression, codec, frame rate all will have a knock-on effect on the video quality. Low bitrate = less quality, frame rate will affect shutter speed.
So there’s tons and tons of variables here.
For example an old GoPro shooting 4K video on a small, old sensor will have to boost the ISO artificially to get good lighting and the old GoPro sensors were notoriously bad in low light. Also remember the shutter speed on a video is limited to the frame rate. At 50fps you can’t shoot at faster than 1/50th of a second because the frames start to overlap.
So 5Dii shooting a still image on a full frame sensor has significant advantage. Larger sensor and bigger lens lets more light in, so can shoot at a lower ISO. A still image could be shot at 1/500th of a second using a fast lens and the AF system is very good so you can get a crisp shot with no noise.
Video and photo will never really be comparable. Just remember that a video is a series of photos in sequence – if you could shoot a video on a 5Dii at it’s full resolution, the camera doesn’t have the RAM and the CPU to cope with the quantity of data passing through it. Even if it were possible, an average memory card would fill in seconds, if it even had the read/write speed to absorb the video.
Hope that helps!