The term Macro technically means larger than life, specifically an image larger than 1:1 magnification. Very few of the lens marked Macro can do this (without additional extension). Nikon uses the term Micro, meaning up to 1:1, and they can focus closely to do 1:1, so it is the technically precise term. Some lenses marked Macro do not even approach 1:1.... (marketing)... much less exceed it.
If you want to see actual Macro work, look here:
http://www.photomacrography.net/forum/
So, there is a huge difference in actual Micro lenses that do focus to 1:1 magnification, and those more like regular lenses, which just happen to focus slightly closer than normal (but still far from 1:1).
1:1 means the image on the sensor is the same size as real life. If the object is 1/2 inch tall, its image on the sensor is also 1/2 inch. This made more sense with film, which we could examine on film. Said another way, if the digital sensor is 12mm tall, then at 1:1 size, the lens will focus closely enough so that a 12mm tall object will just fill it (which is how you prove 1:1 capability).
Focal length does increase magnification, AT THE SAME DISTANCE. 105mm magnifies 105/60 = 1.75x as much as a 60mm (the telephoto effect, enlarges distant subject) - when camera is at the same distance. However, Micro lenses can be used at the same same 1:1 magnification. This means the 60mm lens will be much closer than the 105mm then (because shorter does not magnify as much) - but both can be 1:1, which is Micro. Nikon Micro means the lens will focus as closely as necessary to show a 1:1 image size.
Not all close up work is done at 1:1. A table top scene for example, a scene perhaps 18 inches wide. The 105mm will have to be back near twice as far as a 60mm, maybe 7 or 8 feet back, sometimes not possible in a small room. But the longer lens is great for 1:1 work, allowing more working distance in front of the lens (maybe 6 or 7 inches instead of only a couple of inches). It is a 105mm telephoto lens after all. However, only a couple of inches in front of a 60mm at 1:1 can block the light, the lens in the way of the light.