Phone footage will be good enough for watching back on TV.
(Assuming it’s a modern-ish phone capable of a high definition video, and your TV isn’t the size of an entire room)
4K video is generally what you will want to look for, though my more technologically sound mates would call that rubbish quality
@BertieBotts highlighted the key issue with digital video that as the quality being captured gets higher the file sizes become enormous so some form of compression or other short cuts are needed.
With compression if you compare very old bitmap BMP image files to JPEGs, in BMP every pixel is recorded. So if you have a black picture on 640x480 pixels then your image consists of 30,720 pixels in total stating :
black, black , black etc
Compress that into a JPEG and the file could say:
‘black’, repeat = 30,719
If you have a photo of a black wall with a white cat then there will be a lot of black pixels in a row, some white, lots of black, some white etc
A BMP is the same size no matter what the image
A JPEG is somewhere lower than that. A simple image has a pattern that can be easily compressed to a small size, a complex image is somewhere in the middle
In old school film you would have a series of still photos with x number of photos/frames per second
In digital video you will have the first image, then instead of a new image per frame the file format only saves the changes.
You can sometimes catch out digital video - play a video on screen and it looks good frame by frame, but if you skip 30 seconds then it can’t just display the frame at the 30 second point but has to work out the difference - sometimes you see that you’ve caught it out because the character has walked outside and is on grass, but for a moment you still see a frozen doorway