>>3797994>but I don't understand how or why they would reduce your minimum focusing distance
Because you can focus much closer, with any lens, as long as you can move the lens far enough from the sensor. This quickly becomes impractical because at very close distances, you have to move the lens quite far away from the sensor, and that would need a huge focusing helicoid and barrel, making the lens too big and heavy. So the minimum focusing distance is set by how long a helicoid the manufacturer decided to put on the lens, as a compromise between minimum focus distance vs bulk/practicality.
A macro lens at its most basic is just the same lens with a longer helicoid. Good macro lenses also have an optical design that prioritises performance (in terms of chromatical aberrations etc.) at close range instead of long range. And then, depending on use, you might want a lens which also prioritises flatness of field (say for shooting flat subjects, like film scanning).>Does this depend on the lens you pair them with, or is there a formula involved?
Sure. Here's the simplest case, for a simple lens:
1/(focal length) = 1/(lens to subject distance) + 1/(lens to sensor distance).
As you can see, the longer the focal length, the more you have to increase the (lens to sensor distance) to achieve the same minimum focusing distance.
Also keep in mind that the above "distances" are measured from the optical centre of the lens. For a symmetrical lens, that's roughly the middle of the lens. For a telephoto, it's some point in front of the lens, and for a retrofocal wide, some point behind the lens.
That means for instance a tele would be able to focus closer with less extension than a symmetrical long focal design. Which was one of the reasons teles were invented and used in the old large format days, imagine the feet of bellows you'd need to focus a symmetrical 300mm or 600mm in 4x5" to a close portrait distance.