UTM:
The UTM (Universal Transverse Mercator) grid was created to correct for the convergence of Longitude in that those grid lines are not parallel.  All UTM grids are rectangular and measured in constant meters enabling simpler map presentations.  UTM and the WGS-84 datum are the basis of the GPS (Global Positioning System).  UTM "Zones", shown (HERE), have a letter/number designation for large areas and 7 digits in meters to further define the position in the East and North directions.  UTM zone number and zone character  are used to identify an area 6 degrees in east-west extent and 8 degrees in north-south extent.

Northing is the distance north of the equator in meters and depends on the mathematical shape of the earth as defined by the DATUM and varies about 200m in Northing between NAD-27 and NAD-83.  However, all modern reference systems in the US use NAD-83 as do State Plane Coordinates.  NAD-83 is used, since it considers the North American Continent NOT moving with respect to WGS-84  -which it actually IS.  The USNG is based on the NAD-83 datum where MGRS is based on WGS-84.  (They are functionally identical with an insignificant difference of about 1 meter.)

MGRS:.

Click on this Thumbnail (5MB)

MGRS-2 in the US (MGRS is actually world-wide)

From UTM the MGRS (Military Grid Reference System) grid was created for military purposes to further simplify the position coordinates.  This simplification uses two letters to designate general areas (smaller than UTM Zones) thus reducing the number of digits needed to state a position to 5 digits of meters in the East and North directions.

The system uses a set of  two alphabetical characters for the 100 km grid squares, thus reducing more the number of digits required to be reported.  Starting at the 180 degree meridian the characters A to Z (omitting I and O) are used for 18 degrees before starting over. From the equator north the characters A to V (omitting I and O) are used for 100 km squares, repeating every 2,000 km.  Northing designators normally begin with 'A' at the equator for odd numbered UTM easting zones.

An MGRS coordinate is usually full 10 digits, such as:  13T  DG  97570 38927, which to an untrained person looks complex. MGRS is usually not truncated.  Using 10 digits is impractical since most maps and GPS are not accurate to that level of precision (one meter), and short pairs of numbers are easier to remember and say or copy over the radio.

Further reading: http://en.wikipedia.org/wiki/Military_grid_reference_system

USNG:
USNG uses the MGRS system with the final digit truncated to a precision of 10m (the Approx. accuracy of GPS systems in the US), 100m or 1,000m.  Thus, 13T  DG  97570 38927 is truncated to  9757 3892, or  975 389, or 97 38 in the USNG system.  Using the truncated system simplifies reporting positions verbally and is simpler to plot on a map.  If creating a waypoint in a GPS, the last-mentioned digits would be entered as 97000 38000.

The standard is here:  http://www.fgdc.gov/usng

A valid MGRS or USNG coordinate must always contain the 1 Km grid component.    Which is 97 38 for this example.    These are the principal digits.  No USNG coordinate represents a point, but rather an area.  Any truncation from the left is only to the 13T and DG components when users are trading coordinates with each other inside the same area.

Call in a helicopter from out-of-state, you must use full coordinate due to different Grid Zones.  Call in a helicopter from your base, after a pre-ops meeting in the morning which clearly established your area of operation all day to be within 13T DG, and you could just use the numbers  9757 3892 or 975 389 or 97 38.   That is an example of truncation from the left.   As stated, the trained user has to understand what they are doing and know whether or not the recipient does too.    This is advantageous to fire rescue / SAR, EMS responders who may operate all day in a 10 Km area.     It may not be beneficial for an average hiker on the AT who must use full coordinates of 8, 6 or 4 digits, always and not truncate from the left.

This grid was created by a citizen's committee in 2001 to become a national standard.  All USA land-based people should be using the USNG.  There was much confusion and operational friction during Hurricane Katrina.  There are THREE versions of Lat/Long (hddd.dddddd, hddd.mm.mmm, and hddd.mm.ss), and writing them or saying them over the radio is not easy; especially when compared to the USNG.

Further reading: http://en.wikipedia.org/wiki/United_States_National_Grid

USNG GARMIN NUVI 500

See these files associated with the National Fire Academy and USNG:
http://www.usfa.dhs.gov/downloads/pdf/campus_map_usng.pdf
http://www.usfa.dhs.gov/downloads/pdf/git_usng_intro.pdf

States are on board faster than the US federal government. FEMA was opposed to USNG for a while; now they are on board, but very slowly.

The grids are referenced on USGS topo maps back to the 1940's.  MGRS and USNG grids are the same as UTM grids for the last five digits of the easting and northing.   However, USGS now makes new maps (above) that are designed for USNG.   In addition, inter operability maps for now 19 states are here:  http://mississippi.deltastate.edu/data/USNG_Atlases/  as example.

USNG is mandated for use in Florida by the Statewide Emergency Response Plan:
http://www.ffca.org/files/public/FFCA_SERP2010_FINAL4.pdf

USNG should be used for E911, package delivery, postal adderessing/mail, vehicle GPS (Nuvi 500) and emergency response.      See this article:  http://www.floridadisasterengineers.org/USNG_Files/FDE_posting1/USNG_GENERAL/Start_using_US-National-Grid.pdf
or here: http://statter911.com/category/u-s-national-grid/

Also see pages 64-71 of this document:  http://www.floridadisasterengineers.org/USNG_Files/FDE_posting1/USNG_GENERAL/CISaddendum(082908)Signed.pdf

http://www.fgdc.gov/usng

http://mississippi.deltastate.edu/

http://www.mngeo.state.mn.us/committee/emprep/download/USNG/index.html

Now don't get lost out there -youall!
jack yeazel