There are direct conversions as already printed for lapping film. So as the abrasive gets finer, the grit rating goes up (220 grit sandpaper is finer than 100 grit sandpaper) but the micron rating goes down (1 micron film is finer than 3 micron film).
The difference is that this measurement is metric and measures the particle size itself rather than how many particles will fit in a certain length. Micron: the size of the individual grit particle, like the grit rating above. Also note that sieved grit can and will contain grit smaller than the actual mesh rating. The problem with this method is that the wire size is sometimes considered 1,000 mesh may mean that each mesh opening is 1/1000 of an inch or it may mean there are 1,000 wires per inch in which case the actual openings in the mesh will be 0.001' minus two wire diamters. If you have a 1,000 mesh, it usually means there are 1,000 wires per inch at 90 degrees to each other, as a window screen is. Mesh: is the size of the mesh that separated the grit below from the grit above.
So for a 1,000 grit abrasive, each little stone is 1/1000th of an inch in 'diameter' (not really round but they take up the volume of 0.001 inch). Grit: is the size of the individual particle.
Those are all standard terms and methods.