UNR thread form and UN thread form are basically same. There is just one point differently. UN thread form is with flat root, UNR thread form is with rounded root having radius of curvature between 0.108 and 0.144 times the pitch. Why UNR external threads have rounded root? The reason is that the rounded thread root has better fatigue strength than flat root.

During 1950s , because of the need of fatigue-resistant safety- critical fasteners, The UNR designation was developed. Basically all externally threaded fatigue-resistant safety- critical fasteners manufacture fasteners with UNR threads not UN threads. There are two reasons, one is UNR thread reduces the rate of crest wear, the other is it improve fatigue-resistant strength than UN thread.

There is no UNR for internal threads . UNR threads only will be used one external threads. As a thread gages manufacture, we only provide UNR thread ring gauges, there is no client asking for UNR Plug gages.

UN External Screw Threads: A flat root contour is specified, but it is necessary to provide
for some threading tool crest wear, hence a rounded root contour cleared beyond the
0.25P flat width of the Basic Profile is optional.
UNR External Screw Threads: To reduce the rate of threading tool crest wear and to
improve fatigue strength of a flat root thread, the Design Profile of the UNR thread has a
smooth, continuous, non-reversing contour with a radius of curvature not less than 0.108P
at any point and blends tangentially into the flanks and any straight segment. At the maximum
material condition, the point of tangency is specified to be at a distance not less than
0.625H (where H is the height of a sharp V-thread) below the basic major diameter.
UN and UNR External Screw Threads: The Design Profiles of both UN and UNR external
screw threads have flat crests. However, in practice, product threads are produced with
partially or completely rounded crests. A rounded crest tangent at 0.125P flat is shown as
an option on page 1720.