Here EPSG:32616 WKT, both are same
PROJCS["WGS 84 / UTM zone 16N",
GEOGCS["WGS 84",
DATUM["World Geodetic System 1984",
SPHEROID["WGS 84", 6378137.0, 298.257223563, AUTHORITY["EPSG","7030"]],
AUTHORITY["EPSG","6326"]],
PRIMEM["Greenwich", 0.0, AUTHORITY["EPSG","8901"]],
UNIT["degree", 0.017453292519943295],
AXIS["Geodetic longitude", EAST],
AXIS["Geodetic latitude", NORTH],
AUTHORITY["EPSG","4326"]],
PROJECTION["Transverse Mercator", AUTHORITY["EPSG","9807"]],
PARAMETER["central_meridian", -87.0],
PARAMETER["latitude_of_origin", 0.0],
PARAMETER["scale_factor", 0.9996],
PARAMETER["false_easting", 500000.0],
PARAMETER["false_northing", 0.0],
UNIT["m", 1.0],
AXIS["Easting", EAST],
AXIS["Northing", NORTH],
AUTHORITY["EPSG","32616"]]
The first (WGS 1984 UTM 33 North) has map units of meters, while the second has decimal degrees. If you're talking about a two-dimensional display, the WGS 1984 (decimal degree) data is often displayed using a "pseudo-Plate Carrée" projection. That is, the decimal degrees are treated as if they're linear units and the features are just displayed. A standard Plate Carrée projection would convert the degrees to radians and then multiply by the semimajor axis or radius of the geographic coordinate reference system.
Depending on software and whether data is in a projected or geographic coordinate reference system, there may be different functions available. For instance, in ArcMap, the Measure Tool can provide planar (projected) or geodesic-based distances if the data frame (map) coordinate reference system is projected.
Best Answer
Edit:
The problem is that ALL projected systems are made to...
or
An accurate measurement projection is for a small"ish" area. Not the entire world.
All this being said. Arcgis will allow (other software do this too) multiple projections into one or different projections.
So you just decide what projection "looks" the best for your map, Set the document projection (see previous answer from below) to that. and then load all your data.
The only reqirement is that each data source would need to have a projection defined. (shape files use a *.prj file, tif images use a *.tfw file).
These helper files tell the software what the coordinates relate to. On-the Fly projection does the rest of the work.
I suspect that because of the question you have one or more datsesets that are not overlaying correctly.
If this is true you should look at the prj file to determine if: first there is one; and second if it is defined as the correct projection.
You can search gis.stackexchange for other questions related. LIKE: "projections"
Or just look at the related to the right of this question.
If you look at the TOC (table of contents). You should have a data frame named layers (that is just a default name).
Right click on that and select properties.
Go to the coordinate systems tab and select the UTM zone you want.
Unless you are actually asking about how to show the utm grid (which is in the grid tab [same dialog])
this should do what you want.