Short answer: No, UTM Zone 15 N is not the same as UTM Zone 15 T.
UTM Zone 15 N means the area bounded by:
- east-west boundaries are the longitudes 90° W to 96° W
- north-south boundaries are the equator and latitude 84° N
UTM Zone 15 T means the area bounded by:
- east-west boundaries are the longitudes 90° W to 96° W (the same as UTM Zone 15 N)
- north-south boundaries are latitudes 40° N and 48° N
As you can see, UTM Zone 15 T is 40° of latitude further north than UTM Zone 15 N.
UTM Zone 15T is actually a MGRS (Military Grid Reference System) "grid zone designator."
The MGRS system uses the same east-west divisions as UTM. Each UTM zone is further divided, as explained below:
Each UTM zone is divided into 20 latitude bands, each 8° tall (except ‘X’ is 12° tall), lettered from ‘C’ at 80°S to ‘X’ at 84°N (omitting ‘I’ and ‘O’), so that the zone and the latitude band together make a ‘grid zone designator’ (GZD).
Each ‘GZD’ is divided into 100km squares, identified by a letter-pair (see illustration). Eastings and northings are then given in metres within each 100km square. (source)
So MGRS coordinates end up looking like this:
31U CT 03760 87415, or sometimes the spaces are removed so it looks like this:
31U is the grid zone,
CT is the 100km square within the grid zone
03760 (the first half of the numbers following the letter-pair) is the easting
87415 (the last half of the numbers following the letter-pair) is the northing
The two-letter grid zones for grid zone designator 15T look like this:
What is unclear from your description, is whether the easting and northing should be using the MGRS coordinate system, or the UTM system:
In the MGRS coordinate system, as measurements from the origin of each two-letter square.
If they want the coordinates collected in MGRS, it's probably easiest for you to collect the coordinates in a geographic coordinate system (IE as latitude and longitude), then convert then using a separate converter tool.
In a hybrid of the UTM and MGRS systems, as measurements from the origin of Zone 15 T
If they want the coordinates collected this way,
- Measure your eastings in UTM zone 15 N.
- Measure your northings in UTM zone 15 N, then subtract the distance (in meters or feet, whichever you're using) between the equator and 40°N.
Note: Before you proceed very far with your data collection, I highly recommend testing out your coordinate collection and conversion method. Use your method to find the coordinates of a known point, then use one of the linked conversion tools to convert it to lat/long. Paste the lat/long in Google Maps (or similar tool) and make the location is correct.