Grid convergence is the angle between true north and the grid north. It varies from point to point except in cylindrical projections, for which all meridians are parallel. For conic projections the meridians all radiate from a central point (off the map to the north in the Northern hemisphere), making it clear the convergence changes as you move in an east-west or north-south direction across the map. For transverse Mercator projections, the grid convergence changes in a more complex fashion, because the meridians are curves joining two fixed points (the projections of the poles).

Tissot indicatrices for ND SP S 83: the red lines point towards true North.

Within the southern part of North Dakota, the grid convergence for the State Plane projection ranges from 2.6 degrees in the southwest corner (meaning that a bearing towards true North would appear to be 2.6 degrees East of North on the map) to -2.9 degrees in the southeast corner. For the UTM projection, the convergence varies from 3.65 degrees to -1.75 degrees in the southeast corner. On average, the UTM convergence is approximately 1.1 degrees greater than the State Plane convergence.

Tissot indicatrices for UTM Zone 14 North: the red lines point towards true North. They tend to point about 1.1 degrees further towards the East (clockwise) than their correspondents in the ND SP S 83 map.

I cannot tell you whether this difference is "minuscule" or not, because that depends on your needs, but given that a 1.1 degree error translates to about 2% of the distance when locations are given as bearings and distances, this seems like an enormous discrepancy for surveying purposes.