UTM is the acronym for Universal Transverse Mercator, a plane coordinate grid system named for the map projection on which it is based (Transverse Mercator). The UTM system consists of 60 zones, each 6-degrees of longitude in width. The zones are numbered 1-60, beginning at 180-degrees longitude and increasing to the east. The military uses their own implementation of the UTM system, called the Military Grid Reference System (MGRS).
One system is no more or less accurate than the other. They are just two different ways of positioning a point. Many experienced users prefer UTM over latitude/longitude when using 7.5' topographic quadrangle maps. Ocean-going sailors and other marine users almost always use latitude/longitude because navigation charts are optimized for this method.
Learn more: The Universal Transverse Mercator (UTM) Grid