Terms like "fat bike" and "road bike" are far to general and not helpful. There are "road bikes" designed to be delivery vehicles in cities and one designed for casual riding on flat terrain and there are ones designed for trail use, i.e. "gravel bikes", and ones for triathalons and ones for road racing and ones for touring.

When it comes to tires the pro riders have been moving to 25mm tires as they have come to realize that the rolling resistance is negligible. The rims that are put on the bikes at the factory are expensive to change out and largely determine who wide a tire can be mounted. I have wheels that allow for 25mm max tire width and others that are OK for 30mm wide tires and my mountain bike rims are fine up tires up to 2.5 inches in tire width.

Fat tires are used on the folding e-bikes as they are much smaller in diameter and so the entire bike fits into a much smaller shipping box. The greater width is required to provide enough air volume to support the weight of the bike and the rider.

At least in the USA road tire widths are metric and mountain bike tires usually in inches as with 27.5 and 29 inch tires and widths also expressed in inches. This is too complicated for some pedantic individuals to understand but it is what it is.