No, mesh corresponds to a theoretical sieve number once you get to particle sizes too small to construct an actual sieve. A 10 mesh sieve would be a screen having 10 holes per linear inch or 100 holes per square inch. Allowing for the wire diameter, a 100 mesh sieve will drop particles with a diameter less than .0059 inches or, if you converti it to metric, 150 microns. After a certain point (about 300 mesh) the wire size becomes problematic and the wire starts taking up more space than the holes and it becomes impractical to build finer screens. 200,000 mesh would be a seive with a screen having 200,000 holes per linear inch. Virtually impossible to build even if you could find wire fine enough to make such a screen. Here's a mesh to micron chart
http://www.showmegold.org/news/Mesh.htm For really tiny particles, they find the size by some other means (there are dozens of methods) and then calculate an equivalent mesh size.
Grit is a number assigned by any one of a dozen different industrial standards committies (ISO, ANSI, CAMI, JIS, FEPA, DIN etc.) Each one gives a formula based on particle size, volume, packing density or some such, as well as a statistical error range, (sometimes adjusted for the difficulty of measuring finer particles so as to allow more slop on that end or to compensate for needle shaped grains when your grit size is based on the diameter of round particles). For normal distributions see
http://bmj.bmjjournals.com/collections/statsbk/2.shtml
Generally, a grit number designates a mean particle size and each standard allows variations within a standard deviation from that mean (sometimes, plus a slop factor).
If I remember correctly, sandpaper goes by the Cami standard and has the biggest error margins. Everyone was asking about Japanese waterstones a year or two ago so I spent a couple of months digging around trying to find the Japanese Industrial Standard grit formulas (found them but wasn't going to pay $60 for a pdf of a standards paper in a language I can't read), but I did manage to find a chart on the web site of a Japanese abrasives manufacturer and created a web page out of it
http://members.cox.net/~yuzuha/jisgrits.html (this table is based on a more recent 1998? standard that specifies measuring particle size by an electrical resistance method... the older standard was based on flotation and allowed slightly larger particles than the current grit numbers)
column one is the JIS grit number, the second is the mean particle diameter, the third specifies the range, the third is the absolute maximum (if a single particle is found that is larger than this, the entire batch must be resorted) and the last two columns give the 3% error limits.
So, if you order a ton of JIS 1000 grit aluminum oxide abrasive and plot the particle sizes on a gaussian bell curve, the mean would be 11.5 microns, with an error of 1 micron so the majority of the particles fall between 10.5 and 12.5 microns (some standards say 50% of the particles must fall in this range, others specify those numbers as the 1 standard deviation from the mean point so 68% would be in that size range). No particle in a batch of 1000 grit abrasive can be bigger than 32 microns (if one is, you can reject the batch as defective). The last two columns in the chart show the 3% limits, so 97% of the particles have to be larger than 7 microns and 97% have to be smaller than 27 microns (if more than 3% are between 27 microns and the max of 32 microns, you can again reject the batch as defective and send it back to the factory)
Basically, the numbers in this chart can be used to draw a bell shaped curve of particle sizes for each grit number and Japanese manufacturers have to grade their abrasives so they fall inside those limits if they want to do business in Japan. Of course, there is nothing stopping manufacturers from trying to get a better reputation by exceeding the standards, or selling premium abrasives (the bell curve would then have the same mean of 11.5 for 1000 grit, but be higher and narrower so a much bigger percentage of the particles will fall in the 10.5 to 12.5 range with much fewer than 3% falling in the abnormally large or small range)
Some grit numbers accidentally happen to be similar to mesh numbers so people often call the mesh numbers grit, but they are different. i.e. 3 micron diamond dust ranges from 2-4 microns and is 8,000 mesh, while 8000 grit JIS is 1.2 microns ranging from 0.9-1.5 microns
For diamond dust in microns
average / range / mesh number
0.1 / 0-0.2 / 240,000
0.25 / 0-0.5 / 100,000
0.5 / 0-1 / 60,000
1 / 0-2 / 14,000
2 / 1-3 / 11,000 (equivalent to a 6,000 grit JIS waterstone)
3 / 2-4 / 8,000
6 / 4-8 / 3,000
9 / 8-12 / 1,800
15 / 12-22 / 1,200
30 / 22-36 / 600 (about 400 grit JIS)
45 / 36-54 / 325
60 / 54-80 / 230 or 235
Here is another useful table comparing sandpaper, European FEPA p- grits and micron sizes
http://users.ameritech.net/knives/grits.htm
Now, you know more than you ever wanted to know and are still confused? So is everybody else ^-^ That is why I just like to go by micron numbers instead of grits or mesh (but even that doesn't help with stones, since the finish a stone leaves on metal depends on the bonding material, grit size, porosity, bond flexibility, bond strength, abrasive friability and the way it fractures... take Arkansas stones for example... they are made from the glass skeletons of sea creatures called diatoms that have been cemented together with more glass / silica, and they have an average diameter of 5 microns. A soft Arkansas is just more porous and loosely bonded while your surgical Arkansas is very non-porous and tightly bonded. One is considered coarse and the other fine, but the abrasive diatom shells are the same size)