And a word on brake pads that are 'too fat'....

When disc brakes were just becoming the normal thing (such as in the early 70's) there was a lot of variance in the making of the calipers and the pads. So pad makers stated making them to fit the thickest application.

So if the pads you bought fit the caliper but were too fat to insert even with the piston pushed all the way flat? You just sanded them down until they slid in.

Primitive? Well, yes, but that was the recommended way to deal with it by the pad makers.