What you said sounds right to me. Other datums are becoming less
important (NAD27 used to matter a lot in the US in the 80s and early
90s, but not so much any more), but UTM and MGRS are still relevant.
Still, projection changes without datum conversion can be implemented
with proj.4, or geographiclib.
The following may be useful:
http://geographiclib.sourceforge.net/cgi-bin/GeoConvert
The author is known for a near-fanatical devotion to correctness, so
it's probably reliable.