Imagine a piece of 35mm film, as used in "ordinary" cameras. At some stage in it's manufacture it is just a flat piece of film with no holes in...
Then it is "formatted". It has a series of holes cut along the edges to enable it to be wound on, mechanically.
A similar type of film was used in older cameras, "instamatics". They also had 35mm film, (in a cassette), and had holes put in one of the edges to allow the film to be wound on, but the holes had different spacing. It was the same 35 mm film but with a different kind of "formatting" You had to use the correct type of film for a specific camera.
Fat and NTFS are 2 types of formatiing for the surface of the hard disk.
It's not exactly the same, but it's the way I imagine it, and I find it helps my mental picture of what goes on inside a disc.
I hope it heelps,