Mechanical hole

Using the same Pad diameter as the drill means that you could have a small sliver for any mis-registration of the Drill and target location. Typically a small pad is defined for allow the Drill chisel cut edge to land, like 0.5mm for a 3mm drill, these Pads need to be defined on, at least, the Begin and End Layers in the Padstack Editor to define the drill depth.

But what does this small pad represent ? If I understand correctly, it's just to define the drill depth, so the effective diameter of the pad doesn't matter, as long as it's smaller than the drill diameter ?

The first thing to determine, is the actual hole going to be plated through or not ? "You don't say"

If not plated then as Oldmouldy suggests you want your pad to be smaller than the drill size. The idea is two fold. In board manufacturer the pad will be drilled away.
The pad also serves as a visual indication of where a drill hole will be on your board so you can actually see it.

The pad width has absolutely nothing to do with the Height.  Z height is controlled by the excellon drill machine setup.

There are other considerations. If you intend to pour some copper consider having a keepout on all layers that use that padstack.

Last thing is any pin on a schematic symbol needs to have a corresponding pin defined on the footprint. It does not matter if they are mechanical holes or not.
Try to keep a 1:1 relationship between the board and the schematic.

Pay attention to inner layers if they exist. For non plated holes. Having a keepout is a really good idea.

Thank you for the detailed explanation, I think I understand !

Thank you for the detailed explanation, I think I understand !