I have a technical conceptual question... if a point is defined as being at 49.908787, -97.204551 in datum WGS84, what are the DD coordinates (______, ______) in datum NAD83 (for the same location)? NAD83 I believe is never displayed in Decimal Degree (DD) format, so it would be indicated as (about) 14U 628914.29, 5530034.77. But can you display the NAD83 coordinates in DD, in which case the numbers would be a little different? I can't even find or figure out a way to make that conversion, I think because it's never used.
Maybe this is not a "real world" problem, but it can happen when importing xy coordinates from a table to points in ArcGIS. For the tool ("Coordinate Table To Point"), you can choose the coordinate system associated with the points ("Input Coordinate System"), regardless of how they are formatted. So if you import coordinates with datum WGS84 and then the same coordinates (in same DD format) imported as NAD83, the output will be off about 2 metres (at least where I'm looking).
So is it important to specify with a coordinate table what the GCS is? Technically yes, otherwise the user has to guess and might be off 2m. Most GIS users would probably assume right, based on the format (DD = WGS84, whereas coordinates with a zone and no or few decimals are NAD83/UTM). But if you're sending to someone who wants the points and doesn't know this, they might assume wrong and be off by a bit, right?
Here is the scenario I am facing. We are sending data to a client. Most of the data are in NAD83. One of the data files is a table of DD coordinates that are WGS84. I convert the table of points to a points shapefile ("Coordinate Table To Point" tool, with "Input Coordinate System" as WGS84). Then I project that shapefile to NAD83, so the spatial reference information is consistent with all the other shapefiles we are sending. But now this shapefile has lat and lon attribute table columns with DD values that are in WGS84 (not NAD83) - potentially leading to confusion for the client, right? If they were to get those attribute table coordinate numbers, and the info they are in NAD83, the locations would actually be wrong.
... in datum NAD83 (for the same location)? NAD83 I believe is never displayed in Decimal Degree (DD) format, so it would be indicated as (about) 14U 628914.29, 5530034.77. ...
No, Longitude and Latitude can have a NAD83 datum. What you have shown is a projected coordinate system which has a NAD83 datum.
Sadly people have a bad habit of calling Long/Lat coordinates WGS84... it might be, but it is better to say a Geographic Coordinate System (GCS) with a WGS84 datum... that differentiates it from a GCS with a NAD83 or even a NAD27 datum